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10:15 a little mistake sir, you took Vn/Un where it had to be Un/Vn hence giving us 1/4 as the limit's answer. Nevertheless, comparison test still held and gave the consistent answer, great video!
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In 2nd question, when checking the convergence of x=1 , you used comparison test. but u took lim n-> infinity 1/(2n-1)(2n), instead of taking x power n /(2n-1)(2n)?
@@harshverma6837 why did sir take vn/un. It should be un/vn. Then the value will be 1/4 then by p series test p=1 and vn is divergence so un... So at x= 1 series should be divergence..
nopes, that interpretation is misleading. i suggest you observe it again. let me simplify, for n+1, its 2{n+1} -1 which is not equals to 2n. (BODMAS) and he wrote 2n+1 which is same as 2{n+1}-1
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Thank u Sir 🎊 Aapko Mai kiss Tarah se Sukriya Kahu. Aapka Video's Mere Exam ME Bahut Helpfull tha. M2, M3, Dono Hi Clear Ho Gya Thank u So Much Gajendra Sir
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Sir it realky helps me alot... And a request to you to upload next videos on this topic as soon as possible.. My exams are near and i have to prepare..
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sir in Q3 u took un = x^n/n^2 +1 but it is does not satisfy the series ......but when it is un+1 term and un= x^n/n^2-2n+2 it satisfy the series.........
Sir your videos are super awesome... But sir you only taught us and it is also written in the book that for comparison test we write Un/Vn but you have mistakenly miswriten it as Vn/Un in last two solution.
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You will get the same result either you put Un/Vn or Vn/Un...i mean the values can vary but the you will get the right result according to comparison test
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Sir as you told in previous video comparision test that the formula is u^n/v^n but here you write the formula v^n/u^n so i am confusing please clarify me
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Sir in the 2nd question you did limit of n --> infinity (Vn/Un) , is it right? i think it should be limit of n --> infinity (Un/Vn)! Please correct me if I am Wrong!
Your are undoubtedly a great teacher and I'm really grateful for your efforts but what's the point of commenting on your videos ...agr doubt wale comments me aap aapna promotion krke chale jate ho.
yes .... i also have doubt about it and then i found it clear by some research ,if we write Un/Un+1 then it will be >1 which is conversent and if write Un+1/Un then it will be
Very doubt on qn 2,3....many things sir had done mistake.... In qn 2, For x=1, lim of summation of Vn is 1 ... That's finite number and +ve,But it should be divergent as p=1 but sir had written it convergent... So is my point correct pls tell me guys!! 🙏🙏
Sir it is not sufficient condition that limit of Un is equal to zero implies Un is convergent. So how can you conclude here that lim Un = 0 => Un is convergent?
Sir I have a doubt, at 13:40 q the whole series is not getting generate by the Un term you have written. I think it should be 1+Un. Correct me if I am wrong.
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Hello
sir wo vn/un hoga? kyuki comparision test main aapne un/vn likha tha.
Sir video blur he
Sir 2nd que x=1 pe Vn upon Un ye galt h apne comparison test m Un upon Vn btaya h
@@deathsnipe1834 the same thing im thinking....
10:15 a little mistake sir, you took Vn/Un where it had to be Un/Vn hence giving us 1/4 as the limit's answer. Nevertheless, comparison test still held and gave the consistent answer, great video!
yes
Agree 👍
dont worry... thats nothing.. u can take both Un/Vn or Vn/Un . because if Un/Vn is finite positive then Vn/Un is also positive finite.
8:30
Agree👍
Sir q2 meh woh joh Un+1 ka part apne Kiya waha kse 2n+1/2n+2 Aya?? +1 aur -1 cancel nahi honge kya???
n = n+1 means it is 2(n+1) - 1 means it is 2n +2 -1 means 2n+1 hope you get it
@@sksahinparvej5500 Thanks G
Sir
In comparison test we have to use
Limit n->infinity Un/Vn
In this vedio why did you use
Limit n->infinity Vn/Un
Mistake Kardi unhone yaga
Either way it's true
by mistake
either way is true na if you take un/vn and get a constant than even if you reverse it you will get a constant only !
Sir ne comparison test ki video mein bola tha ki Uv/Vn ya Vn/Un likho usse koi farak nahi padta kyunki end result mein humein bas ek constant chahiye.
at x=1 i got un = 1/2 which is greater then 0 , so from d alemberts test it become divergent in second q. but by comparisin test it comes convergent
You are honest teacher which gives all topics in free with deatral explanation 🙏🙏🙏🙏🙏
sir, im student of IIT BHU. your videos are very helpful to me.we going to have our endsem exams from next week.Thank you for helping me
Iit bhu which rank you opt
@@xipingpong5165 i don't think there's any mistake. Can you point out any one mistake
अरे सर vn/un नाही आयेगा un/vn आयेगा
Kya Sir App Bhi
Thank you sir...
Apke video dekhne k bd sare confusions clear ho jate ...
Thanks a lot...❤❤❤
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Superb no words for appreciation
Higher Mathematics required teachers like you thank you very mush
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Excellent sir
Sir I can't understand teaching style of tution sir but easily taken from you
sir in comparison test we used to do
(Un/Vn ) but here in this video you did( Vn/Un)
By doing the both we will get same
@@rahulnayak343 no we won't get the same result (un/vn) will give the reciprocal of what sir has written
@@aaravgupta4747 I have done so
huh, wherever i find, they use Um/(Um+1) only
@@bikdigdaddy 😂😂 comparison test Ki bat Ho rhi h..... Un+1 ki nhi
In 2nd question, when checking the convergence of x=1 , you used comparison test. but u took lim n-> infinity 1/(2n-1)(2n), instead of taking x power n /(2n-1)(2n)?
X=1 hai isliye
@@harshverma6837 why did sir take vn/un. It should be un/vn. Then the value will be 1/4 then by p series test p=1 and vn is divergence so un... So at x= 1 series should be divergence..
@@brachiosaurous_3050 yes you are right mera bhi same yehi aa rha h
@@Pallav2023 to Ab kya krna h 🙄
@@brachiosaurous_3050 exactlyy man I also got 1/4 so its divergent right?
Very helpful video!!!
But a small correction
At 7:39 you should write (2n) for(2n-1) but u have written it as (2n+1).
no correction required please check u again ✔✔✔
😂✔
सही कहा आपने
Correct sneha.. there's mistake.
nopes, that interpretation is misleading. i suggest you observe it again.
let me simplify,
for n+1, its 2{n+1} -1 which is not equals to 2n. (BODMAS)
and he wrote 2n+1 which is same as 2{n+1}-1
@@Ginger_Hrn bhai wo 2n-1 hai it's not 2(n-1). Check again
U did the comparison test just opposite to the theory in ths video,u did lim n tends to infinity (Vn/Un) instead of (Un/Vn)
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@@gajendrapurohit kya reply de rho ho aap sir.....ye koi baat thodi na h....vo student doubt Puch rha h or aapko promotion ki lg rkhi h
Sir ......Un /Vn aayega .....na ki Vn/Un
Bhai woh Un/Vn hoga aur uska answer 1/4 hoga jisko p series test se convergent bolte hai....galat hai sir ko glti se kar diye hai....🙄
Kuch farak nahi padta hai uss chiz se. Tum Un/Vn likho ya Vn/Un
Sir, if the ratio test fails then can we apply L- Hospital Rule for solving the limit?? And if yes then how to proceed further??
A counter example to the concepts part at 3:00 would be the sequence 1/n which has a limit that is 0 but the series is Divergent.
Your class on these topics is superb,, it is extremely helpful to us.
Thank u Sir 🎊
Aapko Mai kiss Tarah se Sukriya Kahu. Aapka Video's Mere Exam ME Bahut Helpfull tha.
M2, M3, Dono Hi Clear Ho Gya
Thank u So Much
Gajendra Sir
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Thanking you,

"Quality Education"
Teaching is not proper u should explain the methods instead of just writing it bcoz u know them well
You sure you saw his previous videos of this playlist?
Bhai engineering me itna bta rhe h whi kafi h basic par he dhaan dege to video bhi lambi ho jayegi
sir your viideos are so helpful and u can describe any method very easier and clear way thank u sir
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11:17 why is it vn/un it should be un/vn ...i think it's a mistake please confirm
The last two cases for x=1 , while using comparision test it should be Un/Vn not Vn/Un , correct it please .
Same doubt
Ur right ..
I can be anything just the ratio needs to be constant
This channel help me a lot in my first year b. Tech carrier . It is the best channel for learning maths during graduation. ❤❤❤❤❤❤❤❤❤
Sir it realky helps me alot... And a request to you to upload next videos on this topic as soon as possible.. My exams are near and i have to prepare..
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@@gajendrapurohit simp
Like you said in the last part that we can even use limUn tends to infinity...but then what will be the answer if limUn tends to infinity is 1
Sir in this test some books has mentioned un/un+1 ratio...which ratio is right???
Thank you very much sir.....💞
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Sir please tell a serial wise all the test when we use whose test there are very much confusion
sir your class is very helpful for semester exam preparation
sir in Q3 u took un = x^n/n^2 +1 but it is does not satisfy the series ......but when it is un+1 term and un= x^n/n^2-2n+2 it satisfy the series.........
Sir you are the best teacher
इतना आसान सरल तरीके से कोई नहीं समझा पाया था धन्यवाद सर
सर् आप महान हो
Sir your videos are super awesome... But sir you only taught us and it is also written in the book that for comparison test we write Un/Vn but you have mistakenly miswriten it as Vn/Un in last two solution.
Sir app bhut badiya sir h app apne bhut yogadan diya
Sir ek jagaha par comparison test main lim(un/vn) lian hain aur ek jagahapar lim(vn/un) ... Kya ea dono sahi hai....???
Yes
Sir very nice, and important
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Your videos are really very helpful
i usually hate when ytubers bheekh maangte hai likes ki but ye bnda fr bhii genuine hai ....good job sir ...aage 4saal btech aapke sath hi gujrenge agar aise hi pdhaate rhe
bhai mai bhi fresher hu, kya ye subjets ke lie channels mile tumko?
1. Basics of electronics and communication
2. Basics of Mechanical Engineering
3. Chemistry
agar pta chale kch ache channels toh btana bhai
Thank you so much sir..
Sb confusion dur ho jate h aapk video dekhne k bad.
Sir please proof bhi krva dijiye theorem ka 🙏
Exam m proof bhi ata h compulsory
Bilkul sahi bola 😊
Sir book me dalemberts ratio test me Un apon U(n+1) de rka h please btaiye ye Shi h Kya
Thanks sir
Sir mane aapko unacademy par follow kar Liya
Aabh to iit jam chemistry k leya best channel in utube
Sir app sare consept ko clear kar dete hain thanks sir je
sir your channel help me in engineering very very much
sir thank you so much
you have english subtitles for us south indians also
your channel is a gift from god sir
Superb...👍...but why vn/un in D'alembert's test?
Sir iam loving your videos best teacher onli e thank you for such excellent teaching content..... India needs teachers like you sir🙏🙏🙏🙏
Sir for the last sum how is it convergent?? According to comparison test if p=1 then it's divergent right?? Because Vn =1/n^2
Same doubt
p = 2 , so the series converges na
Sir plzz sare theorem se related video v post kijiye
Hello rocky handsome
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Thank you sir ❤️❤️❤️
I love the way you teach and explain the concept easily
sir kya baat hai aap ki !
prayers, appreciation and much love from pakistan
Sir lim Un =0 is a necessary condition for covergence , so we can't say if limUn=0 then sumUn converge
no tha statement what he wrote is wrong ...
Sir if Un/Un+1 then sir Un is convergent when l >1 ?
Great teaching sir
Sir in your previous lecture you have told that there will be Un/Vn and here it is Vn/Un,how??
Right sir we confused 🤨🤨
It's his choice😂
You will get the same result either you put Un/Vn or Vn/Un...i mean the values can vary but the you will get the right result according to comparison test
@@Ramanbhai121 at first i was also confused but after that i checked the method and i got the same result
Agle video mein apne Un/Vn bataya tha lekin ish video mein Vn/Un likha hein .. kiya dono hi true hai ? Agar hai to hum kab kon sa wala lenge...
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@@gajendrapurohit question puchha tha
Sir plz tell me Apne D Alembert test me v/u le rhe ho for comparison test bt pehle wali video me Apne u/v Liya tha for comparison test plzzzz clear it
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Great sir and thank you this very helpful for me 🙏🙏🙏🙏🙏
Thank you sir 🙏🙏
Thanks sir for all types lecture provided by you
Sir aap bahut acha content banate hain.
Thank u Sir..Really your all lectures are out standing
Sir as you told in previous video comparision test that the formula is u^n/v^n but here you write the formula v^n/u^n so i am confusing please clarify me
thanks a lot from the bottom of my heart
Thanks a lot Sr bht bdiyaa
Big fan of teaching method
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Thanking you,

"Quality Education"
Sir bahut simple way explained
You are the best teacher sir
Thank you so much for your hard work for us ❤️🙏
Thank you Sir 🙏
Sir please upload a lecture on Fourier series
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Thank you sir
Sit agar question me konsa test use karna hain ye mention kiya na ho to hum koi bhi test use kar sakte hain?
Thanks so much sir for covering this topic
Sir in the 2nd question you did limit of n --> infinity (Vn/Un) , is it right? i think it should be limit of n --> infinity (Un/Vn)! Please correct me if I am Wrong!
6:36 , 10:28 for remembrance 👍thank you sir
Sir your's video are very usefull for us thank you so much sir
Nice explanation, help me a lot.
Thanku so much sir.
Your are undoubtedly a great teacher and I'm really grateful for your efforts but what's the point of commenting on your videos ...agr doubt wale comments me aap aapna promotion krke chale jate ho.
Bilkul sahi baat hai
Hello
Please reply me
Thankyou sir 🙏🏻🙏🏻
Your video is so helpful for us👍🏻👍🏻🥰
Please upload a video on career opportunities after B. Sc mathematics
Sir app questions k beech m calculation nhi samjaate ho lakin aap bahut achaa padaate ho
Sir , Can we write lim n--> ♾️ Un/Un+1 in place of lim n--> ♾️ Un+1/Un ??
I am so confused please resolve my doubt .
Thanking you
yes .... i also have doubt about it and then i found it clear by some research ,if we write Un/Un+1 then it will be >1 which is conversent and if write Un+1/Un then it will be
whenwe are doing Un+1 , how does 2n-1+1 become 2n+2
Put "n+1" in place of "n" here and solve
Same query 🙂
U are great sir
Happy teacher's day sir
Sir aap bhut accha padhate hai
Very doubt on qn 2,3....many things sir had done mistake.... In qn 2, For x=1, lim of summation of Vn is 1 ... That's finite number and +ve,But it should be divergent as p=1 but sir had written it convergent... So is my point correct pls tell me guys!! 🙏🙏
Sir it is not sufficient condition that limit of Un is equal to zero implies Un is convergent. So how can you conclude here that lim Un = 0 => Un is convergent?
we have a necessary condition that if Un is convergent then lim Un = 0. But it is not sufficient. Wright sir?.
thanks sir
Thank you sir
Your videos are really very helpful
Sir I have a doubt, at 13:40 q the whole series is not getting generate by the Un term you have written. I think it should be 1+Un. Correct me if I am wrong.
Sir question number second me 2n ki jagah n sqare bhi to rkh skte the
Thankyou so much sir ji
At 14:52 Un is cgt when x= 1 hoga naa. Dono cases mein sir ne equal ka sign lagaya hai, issey toh contradict hoga, someone please correct
i got this concept properly thank u sir
thank you so much sir
sir this really really helps a lot.
Sir can you please upload a video of D'alembertz solution of one dimensional wave equation
sir convergent kese aya? x>=1 .It should be divergent and how vn/un possible
Aapka koi jawab nhi hai sir