Alternate:- write 2018/2014 as 1 +4/2014, split it into 4 terms as 1/2014 which when added to 2014/2015 is > than 1 because 1/2014 is > 1/2015 similarly for other 3 terms, all three will become >1 therefore 4terms are >1 and 1term is 1 which on adding is >5
Write 5 as 1+1+1+1+1. Then convert 1 as 2015/2015 + 2016/2016 + 2017/2017 + 2018/2018 + 2019/2019 = 5 Now we can write 2015/2015 as 2014/2015 + 1/2015 Now do this for all the remaining fractions. 2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 + 2018/2019 + 1/2015 + 1/2016 + 1/2017 + 1/2018 + 1/2019 = 5 Hence 5 is greater Hehe
Another method will be to create another term with 2014 in denominator so given expression will be be greater than 5.hence expression is greater than 5
Find number of real roots of the equation sec theta + cosec theta = root 15 real roots of the equation lying between 0and pie sir iska answer har ek jagah alag alag hai
Literally, I solved it in a dito same way in less than a minute (Currently I am in class 11 preparing for 2026 jee). Sir, thankyou so much because when I am in class 10, I started to see your videos and trying to solve your question and learnt so many things
we can also generalise this i took alpha as 2014 and replaced everything with alpha then added and subtracted 1 from all the numerators except the last one, to get the following: 1-1/alpha+1 + 1-1/alpha+2 + 1-1/alpha+3 + 1-1/alpha+4 + 1+4/alpha taking all 1's together {4/alpha - (1/alpha+1 + 1/alpha+2 + 1/alpha+3 + 1/alpha+4 ) } + 5 here 1/alpha+1 < 1/alpha and so on till 1/alpha+45
Sir pls solve this question in very next video: Prove that: (sinA.sin2A+sin3A.sin6A)/(sinA.cos2A+sin3A.cos6A)=(3tanA+2tan^2A+2tan^3A-6tan^4A-tan^5A)/(1-2tan^2A-6tan^3A-3tan^4A+6tan^5A)
LOGICAL SOLUTION: {Desclimer: 2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 =“first 4”. And 2018/2014= 5th one} 2014/2015 is a little less than 1 2015/2016 is a little less than 1 2016/2017 is a little less than 1 2017/2018 is a little less than 1 2018/2014 is greater than 1 @Sum of first 4 is a little less than 4 @ sum of all 5 is= A little less than 4 + greater than 1( BUT NOT LITTLE GREATER,IT IS ONLY GREATER) = If we add X with the sum of “first 4” such that the sum of “first 4”+ X=4 Then we have to subtract X from it [for equal] We subtract X from the “5th one”. Which is greater than 1 Then we will get a little greater than 1 [because X is a very small number] Now , “first 4”+“5th one” =“first 4 +X” + “5th one - X” =4+(1+something) =5+something Hence , it is GREATER thaN 5
Pehle a,b,c ke liye koi bhi value put karo taki a+b+c = 0, phir wahi values (a²+b²+c²)/(b²-ac) mein put kardo For example: a=-1, b=0, c=1 a+b+c=0 ho gaya (a²+b²+c²)/(b²-ac) = ((-1)²+0²+1²)/(0²-(-1)(1)) = (1+0+1)/(0+1) = 2/1 = 2 To agar a+b+c=0, then (a²+b²+c²)/(b²-ac) = 2
2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 + 2018/2014 1-1/2015 + 1-1/2016+1-1/2017+1-1/2018 + 2014 + 4/2014 5-(1/2015 +1/2016+1/2017+1/2018-4/2014) 5-(1/2015 + 1/2016 + 1/2017 + 1/2018 - 1/501) The first 4 terms in the bracket will give a very small number because the denominator has 4 digits So in the answer, the non zero number will be after 3 zeroes after the decimal point. The last term 1/501 will give a relatively bigger number as only 3 zeros in denominator. non zero number will be after 2 zeroes after the decimal point. So the final answer in the bracket will be negative and so the minus next to 5 and before the final answer in the bracket will become + and ans will be > 5
Are bhaiya Maine kitne baar comment kr ke bataya hai ki idhar udhar se question lekr logo ko gumrah Mt Kiya kro. Ye log ek digital board le lete hai or bakwaas krne lg jaate hai. Inko Ghar se koi problem nahi hai.
this video is disservice to students. it is a conceptual question and should be solved in 10 seconds. consider two vectors of numbers (2014, 2015, 2016, 2017, 2018) and (1/2015, 1/2016, 1/2017, 1/2018, 1/2014). your given sum is the dot product of these vectors. now, you are allowed to rearrange the coordinate of these vectors as you wish, before taking the dot products. you get the least value, if you ordered the coordinates of one vector in ascending order and the other is descending order, before taking the dot product. close your eyes and try to conceptually imagine this. You are replicating the largest of the first co-ordinate least amount of time, among all ordering. Conceptually, it should be clear, otherwise search for re-arrangement inequality. so you get the least value, if before taking the dot product, you put one vector in ascending order (2014, 2015, 2016, 2017, 2018) and the other in descending order (1/2014, 1/2015, 1/2016, 1/2017, 1/2018), take their dot product and you get 5. so the dot product in any other arrangement, specifically in the given arrangement, will be at least as much as the least value, therefore you get your result. BTW, if you close your eyes, you can show that the max value you get if you ordered the co-ordinates in the same monotonicity order, therefore, tell me which is bigger in 5 seconds. A. 2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 + 2018/2014 OR B. 2014/2018 + 2015/2017 + 2016/2016 + 2017/2015 + 2018/2014 you have 5 second to give the answer. A or B? which is bigger?
Abe o hasne wale Sabse pehla number 2014/2015 yaani less than one. Sabse last wala number 2018/2014 yaani greater than one. Ho gaya 2 number different. Yaani equality hat gaya.
Sir i did it in following way :- (2015-1)/2015 +(2016-1)/2016 + (2018-1)/2018 +(2014+4)/2014 =4-1/2015-1/2016-1/2017- 1/2018 +1 +1/2014+1/2014 +1/2014+1/2014 .. It can be firther written as 5+ 1/2014-1/2015 + 1/2014-1/2016 +1/2014 -1/2017 +1/2014 -1/2018 . As 1/2014> 1/2015 ,16 , 17 ,18 Hence there should something positive... And from here 5 + positive something is greater than 5
Let expression is ∆ = 2014/2015+2015/2016+2016/2017+2017/2018+2018/2014 =2014/2015~0.999 =2015/2016~0.999 =2016/2017~0.999 =2017/2018~0.999 =2018/2014~1.00.......somthing Sum 0.999+0.999+0.999+0.999+1.000=4.996...somthing So ∆
Alternate:- write 2018/2014 as 1 +4/2014, split it into 4 terms as 1/2014 which when added to 2014/2015 is > than 1 because 1/2014 is > 1/2015 similarly for other 3 terms, all three will become >1 therefore 4terms are >1 and 1term is 1 which on adding is >5
Maine bhi Kiya tha aise
Write 5 as 1+1+1+1+1.
Then convert 1 as
2015/2015 + 2016/2016 + 2017/2017 + 2018/2018 + 2019/2019 = 5
Now we can write 2015/2015 as 2014/2015 + 1/2015
Now do this for all the remaining fractions.
2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 + 2018/2019 + 1/2015 + 1/2016 + 1/2017 + 1/2018 + 1/2019 = 5
Hence 5 is greater
Hehe
Same thinking
Good teaching is one-fourth preparation and three-fourths pure theatre.” - ❤❤
Another method will be to create another term with 2014 in denominator so given expression will be be greater than 5.hence expression is greater than 5
very nice method sir...
😳
Easy tha, maine khud hi kar liya😊
Find number of real roots of the equation
sec theta + cosec theta = root 15 real roots of the equation lying between 0and pie sir iska answer har ek jagah alag alag hai
This is is amazing................. Process to slove it.
I am very happy with this.😊
Thank you sir for mentoring i got air in 1 baigan exam of aalu sabji😊
AM GM Naam Ki bhi ek cheez hoti hai
@@ChahakRajput bro u r duffer
@@ChahakRajputkuch bhi ?
Sab term cancel hoga
>=5 ayega since all terms not equal hence>5
Maine bhi am gm se kiya
Toh AM calculate krne ki zrurat h hee nhi
Sexy est answer bro
Literally I solved it in a very different and more easy solution in a minute
Class 10th preparing for jee
How much u have completed in all subjects
Literally, I solved it in a dito same way in less than a minute (Currently I am in class 11 preparing for 2026 jee).
Sir, thankyou so much because when I am in class 10, I started to see your videos and trying to solve your question and learnt so many things
Only after second step I didnt even need to do the other steps because I already realizes that 5 is smaller than that
Sir,I think AM GM is best app. Since given sum is greater than or equal to 5 ......and equality is not valid becoz terms are different
bro thats what i did
Sir pls solve integral of whole root 1+tanx dx
In shortest method pls😢😢
Int ( 1+ tanx )dx= int (dx) +int (tanx)dx
=x+ log|secx|+c
@@manthangupta3164 I said whole root of 1+tanx dx
we can also generalise this
i took alpha as 2014 and replaced everything with alpha
then added and subtracted 1 from all the numerators except the last one, to get the following:
1-1/alpha+1 + 1-1/alpha+2 + 1-1/alpha+3 + 1-1/alpha+4 + 1+4/alpha
taking all 1's together
{4/alpha - (1/alpha+1 + 1/alpha+2 + 1/alpha+3 + 1/alpha+4 ) } + 5
here 1/alpha+1 < 1/alpha and so on till 1/alpha+45
Sir pls solve this question in very next video:
Prove that:
(sinA.sin2A+sin3A.sin6A)/(sinA.cos2A+sin3A.cos6A)=(3tanA+2tan^2A+2tan^3A-6tan^4A-tan^5A)/(1-2tan^2A-6tan^3A-3tan^4A+6tan^5A)
What the heck is this
@@mayurpoddar5822 Bro has designed JEE ADVANCED question for 2025.
0:37
Isn't this a one liner by AM-GM?
Thank you sir for uploading all old videos
sir maine 2014 ko split kr ke 2015-1 kr ke and so on sabhi terms ko solve kiya to 1st expression is greater than 5 aaya
thnx for this vid soln.....💗💗
Although there can be any other way but i also solved with same approach
Equal
Bhai AM GM SE KAR LETE
Meanwhile the Calculator exists...
Yeah but if it is solved without calculator then it will be fun
LOGICAL SOLUTION:
{Desclimer: 2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 =“first 4”. And 2018/2014= 5th one} 2014/2015 is a little less than 1
2015/2016 is a little less than 1
2016/2017 is a little less than 1
2017/2018 is a little less than 1
2018/2014 is greater than 1
@Sum of first 4 is a little less than 4
@ sum of all 5 is=
A little less than 4 + greater than 1( BUT NOT LITTLE GREATER,IT IS ONLY GREATER)
= If we add X with the sum of “first 4” such that the sum of “first 4”+ X=4
Then we have to subtract X from it [for equal]
We subtract X from the “5th one”. Which is greater than 1
Then we will get a little greater than 1 [because X is a very small number]
Now , “first 4”+“5th one”
=“first 4 +X” + “5th one - X”
=4+(1+something)
=5+something
Hence , it is GREATER thaN 5
That's what I thought
Good evening sir
Sir i like your videos plz have vudeos on ioqm too
AM GM se bohot easily ho jata
Kesy ho jata sab keh rhy hain AM GM mujhy smjh ni aya
@@hafizusamabhuttabro am>gm ak inequality hai series and sequence me usme dekh lena pta chal jayega 😊😊😊
@@Jai_maa_karny is question ko kesy solve krain agr ho sky to solve kr k bhejna
Sir old video of MATHEMATICAL INDUCTION please
Sir ek question me doubt hai ki a+b+c=0 then find (a²+b²+c²)/(b²-ac) iska answer 2 kaise hai?
Pehle a,b,c ke liye koi bhi value put karo taki a+b+c = 0, phir wahi values (a²+b²+c²)/(b²-ac) mein put kardo
For example:
a=-1, b=0, c=1
a+b+c=0 ho gaya
(a²+b²+c²)/(b²-ac) = ((-1)²+0²+1²)/(0²-(-1)(1)) = (1+0+1)/(0+1) = 2/1 = 2
To agar a+b+c=0, then (a²+b²+c²)/(b²-ac) = 2
😂😂😂
Sum is greater than 5
Sir aap na math ki duniya hi palat dete ho
Sir complex no upload Karo please
Am Gm se ek line me ho jata hai sir🤣🤣🤣
Ek alag method se solve krdiya...
Please take trigo question please please I am commenting on your every video please take trigonometry question
AM GM Inequality Laughing in the Corner😂
OMG :- itne likes 😱
Mama I'm famous
What the hell man!
The worst spoiler I ever got
This comment should not be at the top at any cost,I got a spoiler before reaching the notebook😭
@ssgamer5693 true
Bro you are legend ❤❤❤
When i saw the question, i paused for 10 seconds and after that i got it....
AM-GM supremacy🗿
Btw:Good comment
Good evening sir !
sir, by using AM GM inequality I solved this in less than 30 sec
True 🗿
Maine AM GM inequality se kiya to ho gaya 😊
Pehela thinking e a.m>g.m pe chala gaya😅
Ho jayega am ,gm se bhi
Both are equal !
Yes i have used calculator its 4.997
You can also check (2014÷2015)+(2015÷2016)+......
am>gm
one line ans
Itna sochte kaise ho 😮
2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 + 2018/2014
1-1/2015 + 1-1/2016+1-1/2017+1-1/2018 + 2014 + 4/2014
5-(1/2015 +1/2016+1/2017+1/2018-4/2014)
5-(1/2015 + 1/2016 + 1/2017 + 1/2018 - 1/501)
The first 4 terms in the bracket will give a very small number because the denominator has 4 digits So in the answer, the non zero number will be after 3 zeroes after the decimal point. The last term 1/501 will give a relatively bigger number as only 3 zeros in denominator. non zero number will be after 2 zeroes after the decimal point. So the final answer in the bracket will be negative and so the minus next to 5 and before the final answer in the bracket will become + and ans will be > 5
Are bhaiya Maine kitne baar comment kr ke bataya hai ki idhar udhar se question lekr logo ko gumrah Mt Kiya kro.
Ye log ek digital board le lete hai or bakwaas krne lg jaate hai. Inko Ghar se koi problem nahi hai.
Am >=gm
one second solution by am gm
By calculator it's coming lesser than 5
Please please please continue this series of questions. 🙏
5
this video is disservice to students. it is a conceptual question and should be solved in 10 seconds.
consider two vectors of numbers (2014, 2015, 2016, 2017, 2018) and (1/2015, 1/2016, 1/2017, 1/2018, 1/2014).
your given sum is the dot product of these vectors.
now, you are allowed to rearrange the coordinate of these vectors as you wish, before taking the dot products.
you get the least value, if you ordered the coordinates of one vector in ascending order and the other is descending order, before taking the dot product. close your eyes and try to conceptually imagine this. You are replicating the largest of the first co-ordinate least amount of time, among all ordering. Conceptually, it should be clear, otherwise search for re-arrangement inequality.
so you get the least value, if before taking the dot product, you put one vector in ascending order (2014, 2015, 2016, 2017, 2018) and the other in descending order (1/2014, 1/2015, 1/2016, 1/2017, 1/2018), take their dot product and you get 5.
so the dot product in any other arrangement, specifically in the given arrangement, will be at least as much as the least value, therefore you get your result.
BTW, if you close your eyes, you can show that the max value you get if you ordered the co-ordinates in the same monotonicity order, therefore, tell me which is bigger in 5 seconds.
A. 2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 + 2018/2014
OR
B. 2014/2018 + 2015/2017 + 2016/2016 + 2017/2015 + 2018/2014
you have 5 second to give the answer. A or B? which is bigger?
stop yapping
Sir please come Sandeep Maheshwari Podcast.❤
Sir....." concept of AM and GM inequality "suddenly came to my mind......
Just used and got that the summation of the terms is greater than 5.....
People aplying am gm how will they get to know each term is different. 🤣🤣🤣🤣
Tab bhi valid hoga bro bass equality ka sign haat jayga
@@HARSHKUMARSINGH-hq9uwha to it can be equal to 5 and hence we cannot decide which is greater.
@@Ashutosh-md4wt it can't be equal it will be greater
Equality holds when all the terms are equal 😂
Abe o hasne wale
Sabse pehla number 2014/2015 yaani less than one.
Sabse last wala number 2018/2014 yaani greater than one.
Ho gaya 2 number different.
Yaani equality hat gaya.
Sir i did it in following way :-
(2015-1)/2015 +(2016-1)/2016 + (2018-1)/2018 +(2014+4)/2014
=4-1/2015-1/2016-1/2017- 1/2018 +1 +1/2014+1/2014 +1/2014+1/2014 ..
It can be firther written as
5+ 1/2014-1/2015 + 1/2014-1/2016 +1/2014 -1/2017 +1/2014 -1/2018 .
As 1/2014> 1/2015 ,16 , 17 ,18
Hence there should something positive...
And from here 5 + positive something is greater than 5
Me trying to solve using calculator 😂😂
Statistics also
Trying b4 seeing solution, pls pardon errors(if any). love u sir 😊😊
2014/2015 = 1 - 1/2015
2015/2016 = 1 - 1/2016
2016/2017 = 1 - 1/2017
2017/2018 = 1 - 1/2018
2018/2014 = 1 + 4*(1/2014)
1/2014 > 1/2015 > 1/2016 > 1/2017 > 1/2018
=> 4 * 1/2014 > 1/2015 + 1/2016 + 1/2017 + 1/2018
=> 4 * 1/2014 - (1/2015 + 1/2016 + 1/2017 + 1/2018) > 0 ..........(1)
2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 + 2018/2014 = (1 - 1/2015) + (1 - 1/2016) + (1 - 1/2017) + (1 - 1/2018) + 1 + 4*(1/2014)
= 5 + 4 * 1/2014 - (1/2015 + 1/2016 + 1/2017 + 1/2018)
= 5 + (some +ve value). [ from (1)]
2014/2015 + 2015/2016 + 2016/2017 + 2017/2018 + 2018/2014 > 5 (Hence proved) 😴😴❤❤
OMG this is so easy. Got it. Thank you sir. ❤❤
Log = 🗿
Am gm
Qn khtm
A.M G.M. se 5 sec. main kr lete
But usse video nhi bn pata
Let expression is ∆
= 2014/2015+2015/2016+2016/2017+2017/2018+2018/2014
=2014/2015~0.999
=2015/2016~0.999
=2016/2017~0.999
=2017/2018~0.999
=2018/2014~1.00.......somthing
Sum 0.999+0.999+0.999+0.999+1.000=4.996...somthing
So
∆