Telescoping Series

This calculus 2 video tutorial provides a basic introduction into the telescoping series. It explains how to determine the divergence or convergence of the telescoping series. It also explains how to use the telescoping series to find the sum of the infinite series by taking the limit as n goes to infinity of the partial sum formula. This tutorial contains examples and practice problems with factoring and partial fraction decomposition with the telescoping series.
Improper Integrals:
• Improper Integrals - C...
Converging & Diverging Sequences:
• Converging and Divergi...
Monotonic & Bounded Sequences:
• Monotonic Sequences an...
Absolute Value Theorem - Sequences:
• Absolute Value Theorem...
Squeeze Theorem - Sequences:
• Squeeze Theorem For Se...
________________________________
Geometric Series & Sequences:
• Geometric Series and G...
Introduction to Series - Convergence:
• Convergence and Diverg...
Divergence Test For Series:
• Divergence Test For Se...
Harmonic Series:
• Harmonic Series
Telescoping Series:
• Telescoping Series
__________________________________
Integral Test For Divergence:
• Calculus 2 - Integral ...
Remainder Estimate - Integral Test:
• Remainder Estimate For...
P-Series:
• P-series
Direct Comparison Test:
• Direct Comparison Test...
Limit Comparison Test:
• Limit Comparison Test
___________________________________
Calculus Final Exam and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/nGq2e61qYrqUh7M Final Exams and Video Playlists: www.video-tutor.net/

[@farhanalam7642]

Thank god Im born in a age where knowledge is so easily accessible. And thank you for teaching us. I have immense respect for people like you who spread knowledge so the rest of us become more aware.

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[@4seth]

​@@mousumimishra4741 School has definitely gotten more accessible for people as time has gone on so I don't agree with this statement.

[@mousumimishra4741]

@@4seth yeah that's what am saying since schools weren't as accesible in the past years exams were easier since less people wrote them so less competition aswell

[@4seth]

@@mousumimishra4741 Less people wrote them because they weren't smart enough to get in without the internet. There are people who have the ability to understand calculus by reading a math textbook. The bar was much higher in previous era's.

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Noble Prize for what? Ok, peace.

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That idea,(notion), is a bit exaggerated.

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@@normanhenderson7300 No its not exaggerated he is literally saving lives out here!

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Lik bleshal man

[@taranmellacheruvu2504]

*Nobel Prize

[@Shosk]

you are a legend.... i just dont have a knack for sequences and series but you just made my day and semester..... thank you all the way from South Africa

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[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for an awesome explanation of the Telescoping Series Test in Calculus Two. Pattern recognition and problem solving increase my full understanding of the Telescoping Series Test. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@msong5336]

I've said this before and I'll say it again. You are a lifesaver. What you explained in 20 minutes, my professor could not in 2 hours.

[@cr7neymar908]

series are literally going to be the death of me. the rest of calc 2 has been so easy up until now

[@mr.prince8701]

students next semester will be happy to have this video.

[@MrHatranpro]

The man is happy.

[@jamalaldin11]

for the last problem, how did you know to start with an-5?

[@erikb811]

it does not matter really. you can start with an-2, that's what i do each time. ultimately, all of those terms will get canceled other than the last term and potentially second to last term

[@jeremygraham7976]

@@erikb811 I've been looking for an answer to that the past eons thank you

[@yuhanliu6338]

He started with it just to show as an example

[@alexiscabrera3882]

@@erikb811 Bro, your a life saver. I've literally been stuck on this for the whole week!

[@arnoldtaiwo5604]

i am so greatful for this thing u have taught all of us it was so helping for me i am so greatful.thnks

[@anthonymason8652]

I know you get this a lot, but good job. You really are great at explaining things concisely. Which helps those of us just learning the information for the first time. Cheers.

[@karlgrant9923]

How do you know what number to do for An-#? Don't get why we did An-1 on one problem but An-2 on another

[@mathewvonhouzen5468]

This guys videos are very helpful but he does this often. Very small steps in the problem he won’t explain and you see him apply it differently for different problems, but he still won’t mention it

[@marin9207]

My logic on the last problem is that once it starts repeating I counted at how many terms it repeated. This number was 3 [ ]'s. So then I always do 1- that many terms, and this is how I determine the exact amount of an-x terms that I would need. I also observed that it will always involve the first numbers in the bracket for the first listing and the last numbers in the brackets for the an-x listing. I know my explanation sounds confusing but hopefully, someone finds it helpful.

[@patrickibrahim8760]

at 2:28 why did you use n-2 not n-1 or something else?

[@discord_got_hacked2014]

omg perfect timing, we're learning this in my calculus class now

[@gartyqam]

same

[@michaelharley8020]

at 2:20 could someone explain where a sub n-2 comes from? been trying to compare this video with lecture notes and cant seem to find an answer anywhere

[@t2gamerz4]

you are better than my university's professor

[@kitkatgomap3356]

You deserve Nobel Peace Prize for students✌️.

[@fullreinhard]

Thank you for this. We went over telescoping series for practically 5 minutes in class out of 2 weeks and its probably going to be on the exam, yer a lifesaver.

[@vritrakanha]

And which class are you in?

[@Korvilon]

On the problem at 11:00, I got the same answer but I didn't want to do the partial so I tried distributing the n first, then splitting the fraction. I ended up getting Sn= 1+ 1/n. Which ended up being 1 meaning it converged. Was what I did mathematically wrong?

[@Freeflyingpigeon]

you are soo...ooo good at explaining stuff.

[@Jee2024IIT]

people who teaches on black screens are gods

[@sethsimumba7]

It’s much better for eyes too. There is one God. The God of the Bible.

[@nitika9769]

IM SO GLAD YOU EXIST

[@Algebrainiac]

This is most likely the easiest method for determining what the series converges to. You just have to be good at partial fractions

[@LongeAntia]

You're too good😊😊😊 thanks im happy more videos please 😊

[@MrMrannoying]

That last one seems very involved. I know this is a telescoping video, but i was trying to see if there was another way to figure out whether it converges or not, and ran into some trouble. Tried integral test but i end up with [ln(Infty)-ln(Infty)]-[ln(1/2)].

[@solenia4101]

At 2:28 can you explain how you got a(sub)n-2?

[@AframYirdaw]

its a term 2 less than the infinity term (a sub n), hes just trying to show there are some terms there that are going to cancel with the last term.

[@code5913]

How do you know which values will cancel out somewhere in the series?

[@yuhanliu6338]

just find a common pattern

[@cyto3338]

i just checked that for the given term, what value of n does it meet it's additive identity, 1/(n+3) met its antimatter at n+2 which is not possible (sum is 1 to n), similarly, others require out-of-the-interval values of n for annihilation

[@selamawitbirhanu7298]

Tnx alot But I didn't get the point @20:39 why is (1/n+1- 1/n+3) considered as our last term

[@selamawitbirhanu7298]

Ok I think I get it It is because the given telescopic sequence is given as (1/n+1 - 1/n+3) so we have to consider it as our last term right🤓

[@dextermorgan4582]

I understand when we put values in for a1,a2,a3...etc. But how and why do we start putting in, n-2, or n-1, An-5? is there a video that explains this process?

[@Kj-mf6sy]

because we want to see if terms near the end will cancel out, that's why you do n-2 and n-1 to see if they have terms that cancel out too. Hence why its called a telescoping series cause it starts to collapse in on itself but you cannot automatically assume it cancels for every term. So he's showing that some terms are left uncancelled at the end

[@learnteluguwithme821]

At 19:23, is there a reason why you begin at an - 5? How far should we start to see how the terms with a variable in it cancel out?

[@cpotisch]

He isn’t being remotely rigorous so there’s no hard and fast rule as to where you should start when you’re looking for a pattern like this. If you want to save time and have a result you can trust, just keep it in summation notation, break up the sum, and manipulate the index so that it cancels. Far less ambiguous that way.

[@clashmini7747]

No he is just making sure that he knows exactly which terms cancel and which don't you can start at any number like I did at an-3

[@sahildesai4221]

Thanks...you saved me

[@haziqinayat7006]

Can someone please tell how do we get to know when to use an -1 ,an-2 or an-3

[@MrNano-h6j]

do you know that in my country we study lessons of college to inter the college :) and yeah you are saving me now ...thank you a lot

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@@ousali1340 morocco 😊

[@haolekegs696]

where does a(sub)n-5 come from? Confused

[@MiaaMestiza_]

He picked a term far enough from the end of the series [a(sub)n] just to show us what is going on towards the last few terms as the series approaches a(sub)n. You can pick any a(sub)n-k (where k is any natural number) and continue the calculations as so a(sub)n-(k-1) until you reach a(sub)n-1 then ultimately a(sub)n which should be the last term.

[@razabazal4669]

I never thought my dumbass would understand calc 2 and yet here i am. If i can do it, anyone can i promise

[@komiliee]

He just an excellent math teacher. He give good lectures plus good exercises. I do love watching him

[@ARTDEVGRU247]

for the first problem, wouldn't the 1/n+2 technically cancel if you were to add one more sequence?

[@jeremygraham7976]

You don't specify why you use and an A sub n-1 or an Asub n-2 term

[@JaiveerSingh-bg2fp]

How beautifully this man has explained so complex thing. Respect❤❤

[@t2gamerz4]

Love you Man!!!!! awsome

[@omarayoubi8135]

You are hero ❤😭

[@TheNutYT]

I was staring at my paper utterly dumfounded lol... thank you!

[@nataliep1298]

The way I understanding this instantly but look at my professor like 🗿

[@komiliee]

Is it possible to know his name so that we can follow up with him

[@JasonFoo1653]

13:44 Wait why does (n+1) goes first then (n+3) shouldn't they be switched?

[@momozuke2757]

Why can no one offer any explanation as to how you’ll know certain terms cancel out? I don’t see the pattern and I’d appreciate it if someone pointed it out before just telling me it is cancelling out eventually and taking your word for it.

[@zachp8752]

@@Brad-qw1te Unless they failed I guess...

[@lucasargandona4658]

Why does the textbook like to write with i's? Is it necessary?

[@antoniomele436]

Thank you!

[@kuulezechariah9196]

very good brain storming

[@mostafaaamer_maths1705]

good work❤❤

[@Sarah._.s889]

You deserve an award . Seriously, you are the best in all your videos

[@gsbgamesyt575]

You are absolute amazing I love this explanation!!!

[@jayeshparmar2603]

Last example was 🔥🔥

[@shashankreddy2364]

sir in the question two they have given n=1 to infinity then why have you taken n=-1 to find the value of b

[@cpotisch]

Because partial fraction decomposition has nothing to do with the sum and holds for any value of n.

[@ds.44]

Really brother , you explained so well , such that u cleared my doubt in once❤❤❤❤❤❤❤❤

[@nouhounsylla3862]

Hello i have one question. How did find (n+1)(n+3)

[@Sovereign.Indi31]

How do you know how many terms you need?

[@MaharaMsefula]

I think for a telescopic series only until som terms start to cancel

[@MaharaMsefula]

Sometimes you just stop where you feel like the canceling pattern is observed

[@valentiabusi436]

Thanks sir

[@marcelosalazar9040]

Thank you sooo much all your videos help a lot!!!

[@nihatdonmezov8354]

I hope you never quit youtube

[@mohammedthaier1718]

4:50 If n goes infinity, how did it becomes 0?

[@nihatdonmezov8354]

1/infinity is 0. If you divide 1 by a very large number, u are gonna get a very small number. In fact, as n approaches infinity (large number), result is gonna approach 0

[@jacksonr260]

So helpful sir. I can say after this video, I get it.

[@JamesBrodski]

Great video! Thank you so much for making it.

[@baneennabeelaboud8663]

Thank you very good exlpain😎😎😎😎

[@sailaxmi4269]

amazing!

[@Batman-ws9lb]

What happens if we get a series of 2/(n^2-1) which after partial fraction decomposition is 1/(n-1) - 1/(n+1)? What would the S_n be?

[@cpotisch]

Just break up the sum, make a change of index, and adjust the endpoints, and it becomes very obvious.

[@EdrisJohn]

thanks i love you so much

[@akshitasingh866]

are telescoping and difference series same thing in sequence and series

[@radhekumar3919]

Where is that video i need the link of that you told in this video

[@Pages_Perfected]

well, thank you so muchy much 😍

[@keithou4389]

Even if I had access to the biggest library, I'd probably never find out about this. I'm really glad search engines of today is so advanced my pathetic description still pointed here.

[@vishnudevi2661]

Great video MAN

[@josephpoulsen5447]

Thanks for letting me not going to math lab tomorrow. Or math lectures. Or literally anything math related besides the midterms and final

[@sarahchasauce935]

Its seeming like the end terms are always 0 due to the limit of the function being 0. Is this true? Why do we have to look at the end behavior and not just the beginning terms?

[@joeyc2540]

Thank you! This helped me with a tricky problem on my homework!

[@reinaldocomboio6871]

I met you when your channel had at least 300K subs, you re reaching 1 M go ahead man

[@sethgallegos5843]

the last example is only possible if we assume an-7 and an-6... can this only be proven if we write out all 7 terms ?

[@JordanACG]

does anyone know why at 14:07 he used -3?

[@Majeed2003]

what an amazing instructor

[@faith_335]

You are a life savour ♡! Thank you

[@luukvandenbent9453]

Around 8:17, when plugging in n=0 you're dividing by zero besides the series starts from n=1!?

[@aaronchung4541]

He is plugging in 0 to n to find A and B in the bottom equation 1 = A(n+1) + Bn, not into the top equation 1/[n(n+1)].

[@hatrinhhuy2058]

i want to see 1,2 examples with n=2

[@aph5775]

ur single handedly responsible for my degrees ty i owe u my first born

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Lady Zamar is just trying to get Sjava's attention ,the man is innocent .

[@karimogheriano3467]

bro youre a life saver i swear

[@MOHAMEDABDILLAHIARABTKT]

sir what about the series whit no fractions, for example, 1.3.5+3.5.7+5.7.9+.......... if it can not be solved using this method please share whit me a method to solve

[@antoniosayoub4800]

I would die for you😭😭

[@geann6570]

Sir can i have some request?? I am strugling right now in writing a series in sigma notation... can you please make a video on it???:) thanks a lot

[@lechris141]

2:27 why did he take n-2

[@aheedatif6326]

You deserve to be a professor actually teaching in college. My calc 2 professor barely helps me until i understand more and more

[@tino_]

please buy a new mic

[@sebastianpinzonrojas2068]

thank you so much

[@chuz1818]

Thank you sooooo much you are amazing!

[@caghey]

i dont get it, in the previous video when sum was not equal to 0, we said it diverges. why this time when it equals to a number we said it converges??

[@JPL454]

It converges if the sum is a finite number (like 0,5,-7,...) it diverges if it is +♾️ or -infinite

[@rabiekarouia7997]

Removing the red point left in 4:10 is so SATISFYIIING!

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goat my savior

[@agakor]

Thank you

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thanks

[@sciencific3692]

Buddy you are more than god for me, as my guru (teachers)💌