4:50:13 Sir triple sigma wale question mein ham ye bhi to kar sakte hai ki At a time i=1 j=2 k=3 honge kyuki i=j=k allowed nhi hai Btw ye karke mera answer sahi aa raha hai
𝐓𝐈𝐌𝐄𝐒𝐓𝐀𝐌𝐏𝐒 0:34 Nature of Chapter 2:13 Weightage 2:42 *Index* 3:02 *Critical Topics* 6:30 *What is the meaning of nᵗʰ term of a sequence?* 9:57 *Arithmetic Progression* 10:32 General Term of AP 14:18 _🚬 AP is all about a & d_ 23:04 _🚬 Try Rationalization if you see roots_ 27:53 Term from the End 34:45 *Sum of n terms of AP* 41:22 _Standard Question_ 49:20 NOTE (If Sₙ = An + Bn² then B=d/2) 51:34 NOTE (aₙ = Sₙ - Sₙ₋₁) 53:33 *Common Terms* 57:09 Method to find 1ˢᵗ Common Term 1:01:15 Last Common Term 1:07:41 _Good Question: Find 1ˢᵗ Common Term_ 1:13:44 *Key Points of AP* 1:13:50 1️⃣ 1:13:54 2️⃣ 1:14:12 3️⃣ 1:15:26 4️⃣ 1:20:55 Remark 1:28:29 *Geometric Progression* 1:29:17 General Term of GP 1:29:52 *Condition for AP & GP* 1:33:00 _🚬 GP is all about a & r_ 1:42:58 Imp Concept (Factors of x⁴ + x² + 1) 1:47:46 _Good Question: Info about Length of the sides of Triangle_ 1:54:18 Criss Cross Method 2:02:38 _Using ratio and proportion_ 2:08:06 *Sum of n terms of GP* 2:09:12 Sum of ∞ terms of GP 2:12:41 *Observation:* xⁿ -1 = (x-1)(xⁿ⁻¹ + xⁿ⁻² +…+ x + 1) If n ∈ odd; xⁿ +1 = (x+1)(xⁿ⁻¹ - xⁿ⁻² + xⁿ⁻³ -…) If n ∈ even; (xⁿ +1) doesn't have factors 2:20:49 *Key Points of GP* 2:20:52 1️⃣ 2:21:06 2️⃣ 2:21:59 3️⃣ 2:23:33 4️⃣ 2:27:16 *NOTE:* We don't always need 1ˢᵗ term, we can use any term & begin GP 2:34:01 Increasing GP 2:38:47 *Arithmetico-Geometric Progression* 2:40:57 Sum of AGP 2:45:31 Infinite AGP 2:49:41 _Finding AGP Series_ 2:53:49 _If Product is given_ 2:54:59 *Harmonic Progression* 2:55:50 Condition for HP 3:01:58 Sum of HP 3:02:21 *Arithmetic Mean* 3:02:55 ΑΜ of numbers 3:03:11 ΑΜ’s between two numbers 3:06:53 (In General) 3:10:14 Sum of ‘n’ AM’s inserted between a & b 3:11:14 *Geometric Mean* 3:11:18 GM of numbers 3:12:05 GM’s between two numbers 3:12:49 (In General) 3:16:55 Product of ‘n’ GM’s inserted between a & b 3:18:24 *Harmonic Mean* 3:18:40 HM of numbers 3:18:55 HM’s between two numbers 3:19:18 *Relation between AM, GM & HM* 3:19:44 Relation for any given +ve numbers 3:20:48 *NOTE: When “=” holds true* 3:22:15 3 hints to use AM ≥ GM 3:27:30 Concept of Minimum Value by equalling 3:32:32 Range of x+(1/x) 3:34:25 Conceptual Error in finding Min Value (Don't include constants in AM, GM relation) (Equality doesn't come if all are taken together) 3:38:49 If Product is not Good 3:41:01 Error in finding Min Value (If Equality don't come when all terms are taken together in the relation, then take seperately) 3:47:56 Breaking a term: 3a = a+a+a 3:50:19 Applying AM GM seperately and then adding or multiplying 3:51:56 *Weighted AM and GM* 3:53:31 How is this different from the previous topic? 3:58:15 Shortcut 4:05:22 *Imp Relation: G² = AH* A, G, H are in G.P where A, G, H are A.M, G.M and H.M 4:07:17 *Sigma Notation* 4:10:04 Properties 4:11:24 Don't do this mistake 4:12:18 *Imp Formulas* 4:17:01 When Sigma helps?? 4:21:19 _If big terms come inside Sigma_ 4:29:18 Double & Triple Sigma 4:37:45 If Sigma doesn't help 4:41:43 If Multiple Sigmas are linked, some constraints are imposed on variables 4:50:16 *Method of Difference* 5:00:14 Question similar to AGP 5:04:50 *Vₙ Method* 5:05:34 Product in the Denominator 5:20:09 Factorial inside Sigma 5:27:14 If Recurring Relation given
TIMESTAMPS 0:00 Introduction & Nature of Chapter 2:42 Index & Critical topics 6:18 Meaning of nth term of sequence 9:56 General term of an AP 33:50 Sum of n terms of AP 53:33 Common terms in two APs 1:13:44 Key points of AP 1:28:07 General term of a GP 2:08:06 Sum of n/infinite terms of GP 2:20:49 Key points of GP 2:38:39 Arithmetico-Geometric Progression (AGP) 2:54:58 Harmonic Progression (HP) 3:02:08 AM, GM, HM 3:19:17 Relation between AM and GM 3:51:55 Weighted AM, GM 4:05:22 Relation between AM, GM & HM 4:07:16 Sigma Notation 4:50:16 Method of difference 5:04:50 Vn Method
1:37:45 1:46:05 1:52:16 COME BACK TO THIS 1:58:43 2:02:06 COME BACK TO THIS 2:07:52 COME BACK TO THIS 2:18:12 2:19:42 2:20:37 COME BACK TO THIS (Why in 2n, n and n equal division?)
7:428:319:261:29:18 : (n)th term ka meaning : "an expression in n", jismein n=1 put krein toh sequence ka 1st term milega, n=2 put krenge toh sequence ka 2nd term milega and so on and so forth. •Where n is a natural number. 14:1714:3514:5516:4416:5818:3119:2920:4926:3549:01 : AP is always about i) a (ie first term). ii) d (ie common difference). •Aur jaise hi a and d pta chal gye, aap poori AP likh skte hn •Usually 2 info are given 23:4638:2346:43 (then our focus will be on the values on a and d), but • 22:431:26:05 1:27:43 1:58:28 When only one info is given (our focus will be on reln bw a and d), use that reln. You will get the answer 23:0824:28 : In AP, terms ka difference 'khoobsoorat' hota h (which is definition itself), toh jab bhi mauka mila, terms ka difference bna liya kro 29:4733:37 : (k)th term from the end - AP ko palat do ➡️ new d is = -d. Now proceed 37:2439:37 : Ab info S(n) ke terms mein de denge. Our focus still on a and d 52:055:17:33 : To find (n)th term when S(n) is given : a(n) = S(n) - S(n-1) 55:04 : To find sequence (AP) of common terms of two different APs, find first common term manually (ie a pta lga gya of this new AP), and d of this new AP is LCM (d1, d2). Tada. New AP mil gyi as its a and d mil gye •In good Qs, to find first common term, use general method ie (m)th term of 1st AP = (n)th term of 2nd AP. Express m in terms of n (or vice versa)and see for which smallest value of n, m is a natural no. 1:18:22 1:20:46 1:20:58 1:59:44 : Use when sum is known, thus d is the only unknown...
1:29:29 1:32:59 1:38:15 1:42:27 2:27:31 : GP is all about i) a (ie first term) ii) r (ie common ratio). [Entire focus should be on this] • Once a and r pta lg gye, poori GP pta chal gyi 🌟 2:32:31 2:36:03 2:38:38 : No doubt GP is about a and r, but a need not be first time, it can be any term (will increase efficiency) 🌟 1:48:49 1:49:27 : How to use info that a,b & c are the lengths of sides of a ∆ : 1:55:08 1:53:50 1:58:02 : In Qs involving both AP as well as GP : Use Criss cross method (idea is to reduce unknowns) 2:18:23 2:19:10 2:20:34 : Not everytime readymade GP will be given, sometimes you have to break the expression into two or more GPs and then find their sums individually. 2:23:23 : ⚠️ 2:24:00 2:25:45 : Assume terms like this, when product of the terms is known.
2:39:32 2:40:16 : AGP Sum of AGP : 2:44:28 1 : 2:41:29 - Identify the GP 2 : 2:42:21 - Multiply both sides by common ratio of GP 2:53:50 2:54:52 : In this entire chapter, we study about summations (we are more comfortable in addition), hence try to convert product into addition wherever possible 2:58:17 : HP. Ulta krke AP analyse krlo aur fir wapas HP mein jaane ke liye, reciprocal lelo
🌟 3:22:48 3:24:19 3:26:22 3:30:09 3:50:31 : Hints to use AM - GM reln 3:24:37 3:26:48 : Apply AM - GM reln on "concerned terms" 3:29:24 3:30:28. : AM ki min value GM hoti h, aur wo tab hoti h jab terms are equal. Hence terms ko equal kro aur us equal value of terms ke corresponding AM nikal lo ( 3:31:18 ) 3:29:52 3:32:18 : ⚠️ (Product must be constant) ⚠️ : 3:36:31 3:37:55 : While applying AM - GM reln, don't include constants (Since AM is min and equal to GM when terms are equal so the terms need not be equal to the included constant value. So here equality doesn't hold 3:37:02 ) 3:39:15 : Min value of expression asked, terms +, but product 'accha' nhi h ➡️ 3:39:41 3:40:52 3:48:57 3:50:12. : Tod madod ke aesa likhne ki koshish kro ki product accha bn jaye
4:09:31 : Meaning of SIGMA - Expression mein variable ki value initial se lekar final Tak daalte jaiye aur saare obtained terms ka summation kr dijiye 4:13:20 : 4:14:05 4:15:08 4:15:39 4:22:50 : (Addition poocha tha) Summation krna tha toh sequence ko crack Krna pada (ie write it's general term)... ⚠️ : 4:22:56 : Tukdo mein todo ek hi term ho • then apply Sigma (on the gen. term) from initial value of variable to final value of variable... • 4:15:58 Aage ka kaam Sigma ke results pr chod do... 4:16:44 4:22:42 4:27:32 : Start by seeing if it's AP, GP. or AGP. If none of these, then SIGMA se proceed Krna hi... 4:17:02 4:17:31 4:19:14 4:19:44 4:22:16 4:25:34 4:29:06 : SIGMA helps when general term includes const., k, k², k³. • 4:38:55 5:16:59 : ⚠️ SIGMA doesn't help ➡️ 4:39:17 4:39:48 4:40:50 5:17:15 5:19:14 5:19:44 : SIGMA ko expand karke likho, open krne pr kuch accha bn rha hoga 4:21:44 4:22:06 : SIGMA ke andar bhut bda term aa jaye, focus on simplifying. (Sigma pr chodhna after expressing general term inside Sigma in terms of const., k, k², k³) 4:29:47 4:30:58 4:33:07 4:36:11 4:37:45 4:41:24 : Multiple SIGMAs present, apply brackets bw the SIGMAs... Ab brackets ko solve krte jaiye, taking care of the variable present
Method of Diff. : 4:50:16 4:50:44 4:56:35 4:59:25 : Jis sequence ka sum poocha h it's neither AP, GP nor AGP. Thus, it's a question of SIGMA. But hum directly general term bta hi nhi paenge and that's where MOD comes into the picture. MOD helps us get that general term and then we can open SIGMA using results... 4:51:25 4:53:37 4:56:56 4:59:44 : If difference of consecutive terms is good ( ie their sum can be calculated 4:55:22 4:57:46 ), then we use MOD to find general term 4:58:54
1:13:34 sir there is one more observation or you can say 1 more method that starts by Making an ap with ap1 and ap2 and making an ap with ap2 and ap3 then finding the common terms in both the ap = a and d by taking the lcm of 3 aps provided in question
1:33:37 if variables = iota (root wala -1) then in both caes the final ans will be -ve and even in the que.. but condition hai que mai DISTINCT REAL NUMBERS
3 se divide nahi hone walo ki sum waale Q me 363 tak hi common term liye uske baad 366 aur 369,372 nahi liye shaayad ye by mistake hua hoga par please note down karo ki ye number bhi subtract karne hai 1:07:19
@BATMAN_000_7 bro Ramanujan discovered that earlier but couldn't get enough resources to tell the world that he had found something. Till the time he somehow reached Europe(thanks to that one mathematician
@@Naitik_Barnwal bro I agree with u about Ramanujan but this thing was invented by Friedrich gauss it has a complete different story . In his primary school he was given to find the sum of numbers from 1 to 100 and thus he found this way of solving that and invented the formula for sum of numbers in an AP .
3:44:00 in this question I found the min value of all the terms except f(x), it was 2 and 4 and chose the number b/w it, 3 because that term made it an ap. It was somehow correct.
Good morning sir , sir whether I study from any source I get concise path clearity and approach for questions from you only. Sir thank you soo much for your such efforts. Sir please upload one shot for binomial theorem.please sir.
Sir jab AGP ka general term AP aur GP ke general term ka multiplication hota hai to general term a+(n-1)d.ar^n-1 hona chahiye to kaise a+(n-1)d.r^n assume kiye aap
Thankyou soo much sir for your great explanation...❤ But sir there is a problem in many questions you makes some errors and without properly checking answers move forward mean while me who get totally confused 😕 but sir really thankyou for this gr8 session...💕🎉
The PDF of the session is in the link pinned in the telegram channel t.me/JEEnexus
4:50:13 Sir triple sigma wale question mein ham ye bhi to kar sakte hai ki At a time i=1 j=2 k=3 honge kyuki i=j=k allowed nhi hai
Btw ye karke mera answer sahi aa raha hai
Which is 720 I.e. option b
Thankyou so much sir
When will be aravind Kalia sirs next session in youtube
On 11th september@@sureshshetty7241
𝐓𝐈𝐌𝐄𝐒𝐓𝐀𝐌𝐏𝐒
0:34 Nature of Chapter
2:13 Weightage
2:42 *Index*
3:02 *Critical Topics*
6:30 *What is the meaning of nᵗʰ term of a sequence?*
9:57 *Arithmetic Progression*
10:32 General Term of AP
14:18 _🚬 AP is all about a & d_
23:04 _🚬 Try Rationalization if you see roots_
27:53 Term from the End
34:45 *Sum of n terms of AP*
41:22 _Standard Question_
49:20 NOTE (If Sₙ = An + Bn² then B=d/2)
51:34 NOTE (aₙ = Sₙ - Sₙ₋₁)
53:33 *Common Terms*
57:09 Method to find 1ˢᵗ Common Term
1:01:15 Last Common Term
1:07:41 _Good Question: Find 1ˢᵗ Common Term_
1:13:44 *Key Points of AP*
1:13:50 1️⃣
1:13:54 2️⃣
1:14:12 3️⃣
1:15:26 4️⃣
1:20:55 Remark
1:28:29 *Geometric Progression*
1:29:17 General Term of GP
1:29:52 *Condition for AP & GP*
1:33:00 _🚬 GP is all about a & r_
1:42:58 Imp Concept (Factors of x⁴ + x² + 1)
1:47:46 _Good Question: Info about Length of the sides of Triangle_
1:54:18 Criss Cross Method
2:02:38 _Using ratio and proportion_
2:08:06 *Sum of n terms of GP*
2:09:12 Sum of ∞ terms of GP
2:12:41 *Observation:*
xⁿ -1 = (x-1)(xⁿ⁻¹ + xⁿ⁻² +…+ x + 1)
If n ∈ odd; xⁿ +1 = (x+1)(xⁿ⁻¹ - xⁿ⁻² + xⁿ⁻³ -…)
If n ∈ even; (xⁿ +1) doesn't have factors
2:20:49 *Key Points of GP*
2:20:52 1️⃣
2:21:06 2️⃣
2:21:59 3️⃣
2:23:33 4️⃣
2:27:16 *NOTE:* We don't always need 1ˢᵗ term, we can use any term & begin GP
2:34:01 Increasing GP
2:38:47 *Arithmetico-Geometric Progression*
2:40:57 Sum of AGP
2:45:31 Infinite AGP
2:49:41 _Finding AGP Series_
2:53:49 _If Product is given_
2:54:59 *Harmonic Progression*
2:55:50 Condition for HP
3:01:58 Sum of HP
3:02:21 *Arithmetic Mean*
3:02:55 ΑΜ of numbers
3:03:11 ΑΜ’s between two numbers
3:06:53 (In General)
3:10:14 Sum of ‘n’ AM’s inserted between a & b
3:11:14 *Geometric Mean*
3:11:18 GM of numbers
3:12:05 GM’s between two numbers
3:12:49 (In General)
3:16:55 Product of ‘n’ GM’s inserted between a & b
3:18:24 *Harmonic Mean*
3:18:40 HM of numbers
3:18:55 HM’s between two numbers
3:19:18 *Relation between AM, GM & HM*
3:19:44 Relation for any given +ve numbers
3:20:48 *NOTE: When “=” holds true*
3:22:15 3 hints to use AM ≥ GM
3:27:30 Concept of Minimum Value by equalling
3:32:32 Range of x+(1/x)
3:34:25 Conceptual Error in finding Min Value
(Don't include constants in AM, GM relation)
(Equality doesn't come if all are taken together)
3:38:49 If Product is not Good
3:41:01 Error in finding Min Value
(If Equality don't come when all terms are taken together in the relation, then take seperately)
3:47:56 Breaking a term: 3a = a+a+a
3:50:19 Applying AM GM seperately and then adding or multiplying
3:51:56 *Weighted AM and GM*
3:53:31 How is this different from the previous topic?
3:58:15 Shortcut
4:05:22 *Imp Relation: G² = AH*
A, G, H are in G.P
where A, G, H are A.M, G.M and H.M
4:07:17 *Sigma Notation*
4:10:04 Properties
4:11:24 Don't do this mistake
4:12:18 *Imp Formulas*
4:17:01 When Sigma helps??
4:21:19 _If big terms come inside Sigma_
4:29:18 Double & Triple Sigma
4:37:45 If Sigma doesn't help
4:41:43 If Multiple Sigmas are linked, some constraints are imposed on variables
4:50:16 *Method of Difference*
5:00:14 Question similar to AGP
5:04:50 *Vₙ Method*
5:05:34 Product in the Denominator
5:20:09 Factorial inside Sigma
5:27:14 If Recurring Relation given
Thanks dude
thank you
@@nandinisharma3255 date pr jaogi
Bro how do you got a time to do
Please reply
@@13jeelpatel8e3 to do what
TIMESTAMPS
0:00 Introduction & Nature of Chapter
2:42 Index & Critical topics
6:18 Meaning of nth term of sequence
9:56 General term of an AP
33:50 Sum of n terms of AP
53:33 Common terms in two APs
1:13:44 Key points of AP
1:28:07 General term of a GP
2:08:06 Sum of n/infinite terms of GP
2:20:49 Key points of GP
2:38:39 Arithmetico-Geometric Progression (AGP)
2:54:58 Harmonic Progression (HP)
3:02:08 AM, GM, HM
3:19:17 Relation between AM and GM
3:51:55 Weighted AM, GM
4:05:22 Relation between AM, GM & HM
4:07:16 Sigma Notation
4:50:16 Method of difference
5:04:50 Vn Method
Done and dusted!
Thank you very much sir this will boost my maths marks❤
THE ONE SHOTS ARE MORE LIKE PYQ SOLVING SESSIONS COVERING ALL CONCEPTS
1:37:45
1:46:05
1:52:16 COME BACK TO THIS
1:58:43
2:02:06 COME BACK TO THIS
2:07:52 COME BACK TO THIS
2:18:12
2:19:42
2:20:37 COME BACK TO THIS (Why in 2n, n and n equal division?)
Assume n=2 yu can see that no of terms of the two gp is 2 each i.e. 2n/2
Im just suffering by this chapter and after 2 days I've got u with a brilliant explanation ❤
no doubt this is the best video for sequences and series in youtube
Haa 💯
How much calibre he has as a teacher, just blown by his unparallel excellence... ❤❤
7:42 8:31 9:26 1:29:18 : (n)th term ka meaning : "an expression in n", jismein n=1 put krein toh sequence ka 1st term milega, n=2 put krenge toh sequence ka 2nd term milega and so on and so forth.
•Where n is a natural number.
14:17 14:35 14:55 16:44 16:58 18:31 19:29 20:49 26:35 49:01 : AP is always about i) a (ie first term). ii) d (ie common difference).
•Aur jaise hi a and d pta chal gye, aap poori AP likh skte hn
•Usually 2 info are given 23:46 38:23 46:43 (then our focus will be on the values on a and d), but
• 22:43 1:26:05 1:27:43 1:58:28 When only one info is given (our focus will be on reln bw a and d), use that reln. You will get the answer
23:08 24:28 : In AP, terms ka difference 'khoobsoorat' hota h (which is definition itself), toh jab bhi mauka mila, terms ka difference bna liya kro
29:47 33:37 : (k)th term from the end - AP ko palat do ➡️ new d is = -d. Now proceed
37:24 39:37 : Ab info S(n) ke terms mein de denge. Our focus still on a and d
52:05 5:17:33 : To find (n)th term when S(n) is given : a(n) = S(n) - S(n-1)
55:04 : To find sequence (AP) of common terms of two different APs, find first common term manually (ie a pta lga gya of this new AP), and d of this new AP is LCM (d1, d2). Tada. New AP mil gyi as its a and d mil gye
•In good Qs, to find first common term, use general method ie (m)th term of 1st AP = (n)th term of 2nd AP. Express m in terms of n (or vice versa)and see for which smallest value of n, m is a natural no.
1:18:22 1:20:46 1:20:58 1:59:44 : Use when sum is known, thus d is the only unknown...
1:29:29 1:32:59 1:38:15 1:42:27 2:27:31 : GP is all about i) a (ie first term) ii) r (ie common ratio). [Entire focus should be on this]
• Once a and r pta lg gye, poori GP pta chal gyi
🌟 2:32:31 2:36:03 2:38:38 : No doubt GP is about a and r, but a need not be first time, it can be any term (will increase efficiency)
🌟 1:48:49 1:49:27 : How to use info that a,b & c are the lengths of sides of a ∆ :
1:55:08 1:53:50 1:58:02 : In Qs involving both AP as well as GP : Use Criss cross method (idea is to reduce unknowns)
2:18:23 2:19:10 2:20:34 : Not everytime readymade GP will be given, sometimes you have to break the expression into two or more GPs and then find their sums individually.
2:23:23 : ⚠️
2:24:00 2:25:45 : Assume terms like this, when product of the terms is known.
2:39:32 2:40:16 : AGP
Sum of AGP : 2:44:28
1 : 2:41:29 - Identify the GP
2 : 2:42:21 - Multiply both sides by common ratio of GP
2:53:50 2:54:52 : In this entire chapter, we study about summations (we are more comfortable in addition), hence try to convert product into addition wherever possible
2:58:17 : HP. Ulta krke AP analyse krlo aur fir wapas HP mein jaane ke liye, reciprocal lelo
🌟 3:22:48 3:24:19 3:26:22 3:30:09 3:50:31 : Hints to use AM - GM reln
3:24:37 3:26:48 : Apply AM - GM reln on "concerned terms"
3:29:24 3:30:28. : AM ki min value GM hoti h, aur wo tab hoti h jab terms are equal. Hence terms ko equal kro aur us equal value of terms ke corresponding AM nikal lo ( 3:31:18 )
3:29:52 3:32:18 : ⚠️ (Product must be constant)
⚠️ : 3:36:31 3:37:55 : While applying AM - GM reln, don't include constants (Since AM is min and equal to GM when terms are equal so the terms need not be equal to the included constant value. So here equality doesn't hold 3:37:02 )
3:39:15 : Min value of expression asked, terms +, but product 'accha' nhi h ➡️ 3:39:41 3:40:52 3:48:57 3:50:12. : Tod madod ke aesa likhne ki koshish kro ki product accha bn jaye
4:09:31 : Meaning of SIGMA - Expression mein variable ki value initial se lekar final Tak daalte jaiye aur saare obtained terms ka summation kr dijiye
4:13:20 :
4:14:05 4:15:08 4:15:39 4:22:50 : (Addition poocha tha) Summation krna tha toh sequence ko crack Krna pada (ie write it's general term)... ⚠️ : 4:22:56 : Tukdo mein todo ek hi term ho
• then apply Sigma (on the gen. term) from initial value of variable to final value of variable...
• 4:15:58 Aage ka kaam Sigma ke results pr chod do...
4:16:44 4:22:42 4:27:32 : Start by seeing if it's AP, GP. or AGP. If none of these, then SIGMA se proceed Krna hi...
4:17:02 4:17:31 4:19:14 4:19:44 4:22:16 4:25:34 4:29:06 : SIGMA helps when general term includes const., k, k², k³.
• 4:38:55 5:16:59 : ⚠️ SIGMA doesn't help ➡️ 4:39:17 4:39:48 4:40:50 5:17:15 5:19:14 5:19:44 : SIGMA ko expand karke likho, open krne pr kuch accha bn rha hoga
4:21:44 4:22:06 : SIGMA ke andar bhut bda term aa jaye, focus on simplifying. (Sigma pr chodhna after expressing general term inside Sigma in terms of const., k, k², k³)
4:29:47 4:30:58 4:33:07 4:36:11 4:37:45 4:41:24 : Multiple SIGMAs present, apply brackets bw the SIGMAs... Ab brackets ko solve krte jaiye, taking care of the variable present
Method of Diff. : 4:50:16 4:50:44 4:56:35 4:59:25 : Jis sequence ka sum poocha h it's neither AP, GP nor AGP. Thus, it's a question of SIGMA. But hum directly general term bta hi nhi paenge and that's where MOD comes into the picture. MOD helps us get that general term and then we can open SIGMA using results...
4:51:25 4:53:37 4:56:56 4:59:44 : If difference of consecutive terms is good ( ie their sum can be calculated 4:55:22 4:57:46 ), then we use MOD to find general term
4:58:54
22:00 repeat
24:30 repeat
41:00 repeat
52:00 repeat
1:05:00 repeat
1:12:00 repeat
1:19:00 repeat
1:48:00 repeat
1:56:00 imp concept
2:31:00 repeat
2:36:00 repeat
2:49:00 repeat
3:00:00 repeat
3:44:00 repeat
3:58:00 repeat
4:22:00 repeat
4:29:00 double sigma repeat
4:40:00 repeat
4:44:00 repeat
4:56:00 revise
5:03:00 revise
5:14:53 repeat
5:18:00 repeat
5:29:00 repeat
1:07:51 Common terms Q
1:33:19 Observation Q
1:53:36 AP GP mix Criss cross mtd
2:29:21 Approach
3:41:50 GQ
3:49:48 Todne wala approach (AM>=GM)
5:18:03 Basic approach (Hard to click)
5:20:34 Factorials in sigma
5:27:24 Pattern Variety
1:13:34 sir there is one more observation or you can say 1 more method that starts by
Making an ap with ap1 and ap2 and making an ap with ap2 and ap3 then finding the common terms in both the ap = a and d by taking the lcm of 3 aps provided in question
Thank you sir , in my coaching sir told us to just mug up the formulae and the approaches without explaining them , you have cleared my doubts
Well tell ur coach i want to goal iit not nit
Very very nice lecture sir......really no comparable with other...awesome love yu sir ❤❤❤❤❤❤!
sir i first time seen your video and it was soo god thanks for such an apreciating content
BEST CONTENT EVER I SEEN
bihari english seekle math ke pehle
@@melwinj.c5641 😂😂😂😂aise kaun bezati karta h 🤡
sir reccurence walla sawal done and dusted c is the answer of last question.
sir t-shirt colour exactly matches with board colour 😯😯
Contrast of camera is high & Exposure is low
Sir Thank you very much for Best explanation❤
🙌🙌 Bhai saved my exam ❤❤❤
Hello sir. Please have a session on determinants and matrices!!
Hello sir i am commerce maths student this is not even in my syllabus but just to boost my brain i am studying this
Thankyou 😊
friedrich gauss after casually inventing formula of sum of AP 🗿🗿🗿🗿
📈📈 respect +++
Gauss 🗿🗿☠️
He was in primary school when he invented that 💀
@@target__iit that is just hard lol.
1:47:28. WHAT A SMILE!!
Very Good Practice Done Sir 🙏🏻
Respect button for sir😊😊
Thank you for your valuable content
It helped me gaining confident
1:33:37 if variables = iota (root wala -1) then in both caes the final ans will be -ve and even in the que.. but condition hai que mai DISTINCT REAL NUMBERS
Great session
Thank you Sir(Bhai)
Amazing session bhai
Will complete with sheet and repetition by tomorrow
Thankyou
Keep it up prachi....👍👍
Completed
@@JEEnexus thankyou sir
have some shame...... he isnt ur bhai he is ur sir
@@Imyoursk11ddotell me you don't watch the lectures without telling me you don't watch the lectures
Thanks Bhai for this amazing lecture
Completed ✅ with confidence 💪😄🤟
1:07:33 The answer should be 9525 instead of 9225
Yes
Because of you i was able to cover this chapter within 2 weeks
Brow . 2 weeks?
1:50:00 if a=1,r=2 then a + ar>ar² will not satisfy😢 so it may or may not always be true.
Shera, dhyan se dekho uss part ko... U r getting mistaken, in ur understanding...
Sorry sir
@@JEEnexus aakhir kaar mughe shera mil hi gya 😂😂 shera exposed by Bhai 🔥
Sir ji aap great ho
Aap jaise teachers se samaj ko badal kar rakh diya hai
Sir you are GOD to me , best teacher ever💗💗💗💗💗💗
3 se divide nahi hone walo ki sum waale Q me 363 tak hi common term liye uske baad 366 aur 369,372 nahi liye shaayad ye by mistake hua hoga par please note down karo ki ye number bhi subtract karne hai 1:07:19
thank u sir apke waje se sara concepts clear ho gaye
AP means focus on a and d
that triple sigma question at the end was deadly
Yes 😂
Thanks 😊
Thankyou sir means alot ❤
Give a thumbs up if you want the next session to be on sets relation functions 👍👍👍👍
Already taken bro
No needed
Vedantu channel paai hai
36:25 john carl is that student❤
Ramanujan
@@Naitik_Barnwal Fredrich Gauss my man
thank you very much sir ue lecture helped mee alot , ur wonderful sir
thank you sir is one shot se pehle sigma ke sirf 20% sawaal hote thay pr ab 90% ho rhe hai 🙏🙏 ❤❤
🌸 IIT Bombay❣️
Harekrṣṇaaaaaaaaaa sir thank you so muchhhhhh it was so helpfullllllllllllllllll😊
4:48:56 In this I think set theory would be good explanation for a rather difficult to understand question
Sir please next Definite Integration karwana
H.W destroyed
Since all terms of the sequence are -ve then nth term should also be -ve...
Sare number+ve h... 1 hi -ve h
Hence
Ans = C
Bhai Thora shi se smjha do
@@Aryan-v6e Aryan tum iss sequence ki 4 - 5 terms calculate kro... Then you'll see ki sari terms -ve h...
Or sirf c option hi -ve h 👍🏻👍🏻
Bhai aap em baar 5:35:03 me dekho vahana pr bn=2b n-1 ,Kr ke kuch likha Hai
Aur vese bhe is logic se chle to D option bhe to shi hoga
@@Aryan-v6e ohh sorry.. yes you're right... But solve kar k c hi aata h ...
In 2:50:42 the general terms of AGP must be a^2 , (a+d)ar , (a+2d)ar^2 .... right?? can someone clarify my doubt
Focus on a and d
36:29 ramanujan 😊
No bro , it's Friedrich gauss
@BATMAN_000_7 bro Ramanujan discovered that earlier but couldn't get enough resources to tell the world that he had found something. Till the time he somehow reached Europe(thanks to that one mathematician
@@Naitik_Barnwal bro I agree with u about Ramanujan but this thing was invented by Friedrich gauss it has a complete different story .
In his primary school he was given to find the sum of numbers from 1 to 100 and thus he found this way of solving that and invented the formula for sum of numbers in an AP .
Multiple Sigmas 4:29:27
5:34:44 Sir my answer is not coming in this question, is there a solution for this?
Sir STRAIGHT LINES ka ek session kijiye❤
kalia ji ka dimaag bohot tez kaam karta hai
😂😂
4:56:18 Salman khan bodyguard is also preparing for jee 😂
Sir you are best than my imagination 💞💞
36:24 that student is SHERA ❤
Ramanujan tha wo
Thankyou so much sir for sassion pdf I am greatful for you❤️🙏
Thanks❤❤❤
mera bhai mera bhai ❤❤
Ap means focus on a and d
14:00 Ap a and d ke around revolve krti h focus us per hi hona chahiye
1:10:00
Good session sir. Very Helpful
Yes this one.. 45:31, 50:58 , 53:00 , 1:07:34 , 1:11:42, 1:20:42
3:44:00 in this question I found the min value of all the terms except f(x), it was 2 and 4 and chose the number b/w it, 3 because that term made it an ap. It was somehow correct.
lmao just checked the solution, it is kind of similar. I understand better now, thank you sir.
triple sigma wala concept done and dusted!
5:35:01 Done 👍🏻
How bro
Ye 2 ke power me to koe info nhi De
In which Unacademy batch or course, we can find this lecture? I am a plus student. Pls reply.
38:00
74 ❌️
78 ✅️
Best one shot
4:26:39 sir yaha 1 ki jagah 3 ana chahiye tha na pls reply 🙏🏻
Sir over here 1:07:35 the answer is is 9525 but your answer says it is 9225
Pls check
Same bro even I got 9525😅
Ap= fully focus on a & d 😉😉
Good morning sir , sir whether I study from any source I get concise path clearity and approach for questions from you only. Sir thank you soo much for your such efforts. Sir please upload one shot for binomial theorem.please sir.
Sir jab AGP ka general term AP aur GP ke general term ka multiplication hota hai to general term a+(n-1)d.ar^n-1 hona chahiye to kaise a+(n-1)d.r^n assume kiye aap
DONE AND DUSTED (by this chapter 😭-kitna bada hai)
Done and dusted ❤ sir
Pyaar se log mujhe Bhai bolte hai
helped a lot sir
1:07:40 aswer sahi 9525 hai
Bhai alag satisfaction milta agar sahi answer diya rahta sir ke presentation mein😭😭
Sir ne isme se half question purani vedantu vali video se uthaye hai 😅❤
4:43:00 to 4:50:00 revise it!!!!!!!
Mera Bhai OP
Thankyou soo much sir for your great explanation...❤ But sir there is a problem in many questions you makes some errors and without properly checking answers move forward mean while me who get totally confused 😕 but sir really thankyou for this gr8 session...💕🎉
Sir please make a vedio on permutations and combination
Triple summation recurrence done sir
Sir where is exponential and logarithmic series??is it not imp
1:42:25 , 1:46:12 , 1:52:37 , 1:58:17 2:02:23
Sir which book do you use for jee advanced
Sir indefinite and definite integration please ❤❤❤❤
sir please coordinate geometry
Yessss plsssss
proudly mera bhai
Sir Next Solution of triangle please
2:41:16 sum of AGP
Best ❤