Telescoping Series

[@TheOrganicChemistryTutor]

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

[@kidusbahiru4369]

you deserve a noble prize for saving the lives of many students including me. Thank you a lot !

[@adeeb1787]

Noble Prize for what? Ok, peace.

[@normanhenderson7300]

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

[@thiha8372]

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

[@MarathonFX]

Lik bleshal man

[@taranmellacheruvu2504]

*Nobel Prize

[@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.

[@M_M4741]

if u where not born in this age exams would also have been easier and see competition

[@4seth]

​@@M_M4741 School has definitely gotten more accessible for people as time has gone on so I don't agree with this statement.

[@M_M4741]

@@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]

@@M_M4741 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.

[@M_M4741]

@@4seth yeah but population has risen more than college seats have so someone who was average like 20 yrs back could get a good college relatively easily than today

[@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.

[@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?

[@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.

[@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

[@gartyqam]

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[@04agnishikhamajumder24]

@@gartyqam What about you, are you a king/ queen?

[@gartyqam]

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@@gartyqam don't every buy a tesla, use paypal, or go to mars then

[@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.

[@komiliee]

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

[@Sarah._.s889]

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

[@cr7neymar908]

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

[@rabiekarouia7997]

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

[@cameroneinstein546]

thanks dude, you just helped me pass my calculus based astrophysics exam for the first year in Australian National University

[@Jee2024IIT]

are you literally one minute ago?

[@cameroneinstein546]

@@Jee2024IIT huh?

[@Jee2024IIT]

@@cameroneinstein546 nothing

[@JaiveerSingh-bg2fp]

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

[@aph5775]

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

[@mr.prince8701]

students next semester will be happy to have this video.

[@MrHatranpro]

The man is happy.

[@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

[@discord_got_hacked2014]

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

[@gartyqam]

same

[@jahanbayramova739]

Love you💚. You just explained my whole Calculus semester

[@katiele7755]

bless your heart! you simplified this for me in the best way possible!

[@Majeed2003]

what an amazing instructor

[@karimogheriano3467]

bro youre a life saver i swear

[@sabakandashvili5373]

YOU, SIR, ARE MY SAVIOR! THANK YOU SO MUCH!

[@aheedatif6326]

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

[@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

[@TheNutYT]

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

[@jayeshparmar2603]

Last example was 🔥🔥

[@kitkatgomap3356]

You deserve Nobel Peace Prize for students✌️.

[@carenkiptoo7531]

3 years later and you've helped me big time

[@gsbgamesyt575]

You are absolute amazing I love this explanation!!!

[@ioourz]

لولاك ضعنا ياخي 😔❤️❤️❤️❤️❤️

[@ds.44]

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

[@queenkavutha1356]

You are indeed a savior

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I hope you never quit youtube

[@sciencific3692]

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

[@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.

[@yangapeter4649]

You're a savior.

[@marcelosalazar9040]

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

[@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.

[@wal7]

​@@sethsimumba7No, Allah is God, the only one that will save lives from hell

[@JamesBrodski]

Great video! Thank you so much for making it.

[@MHF-go9sd]

Thank you for explaining everything in a very simple way!

[@t2gamerz4]

you are better than my university's professor

[@faith_335]

You are a life savour ♡! Thank you

[@jacksonr260]

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

[@vishnudevi2661]

Great video MAN

[@Freeflyingpigeon]

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

[@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!

[@razabazal4669]

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

[@mouaad2322]

You explain way better then my 'professors' at uni.

[@youbeyou9769]

IM SO GLAD YOU EXIST

[@theesunnlightt2268]

Very helpful and informative! Thank you!

[@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

[@jrim5265]

EXCEPTIONALLY GOOD

[@nataliep1298]

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

[@areeb6703]

Was a little confused. Thank you so much for a well structured explanation!

[@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

[@ousali1340]

انتي عربية بس من اي دولة؟

[@MrNano-h6j]

@@ousali1340 morocco 😊

[@patrickibrahim8760]

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

[@peskyfox97]

Thank you so much! My classes are online now because of COVID-19 and it's hard to understand the class material. These videos are extremely helpful.

[@LongeAntia]

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

[@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

[@evounemilyb7676]

Thank you for this video. It helps a lot!

[@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

[@PhoenixJobio78]

You can do any, it’s just to show how you can cancel these terms. You must know the first and last terms, however

[@quamzgraphix9826]

You are the best.. thank you very much

[@Arnoldshwazeneger]

Wow the last example was a good one

[@gilma4328]

you are the best! Thank you so much.

[@mathsolar7365]

Simple steps, nice...

[@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.

[@josephpoulsen5447]

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

[@chuz1818]

Thank you sooooo much you are amazing!

[@sweatydino7600]

goat my savior

[@Algebrainiac]

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

[@sahildesai4221]

Thanks...you saved me

[@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?

[@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

[@omarayoubi8135]

You are hero ❤😭

[@t2gamerz4]

Love you Man!!!!! awsome

[@iam_epa]

Dude u always save me😂😂😂

[@SN-ow1bp]

awesome video

[@nikkishirazi7292]

THANK YOU SO SO 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.

[@mostafaaamer_maths1705]

good work❤❤

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thank you u r the best

[@kuulezechariah9196]

very good brain storming

[@Pages_Perfected]

well, thank you so muchy much 😍

[@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)].

[@benjiaaazhang9249]

Life saver!

[@JasonFoo1653]

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

[@karimagulshan1814]

Thank u very much sir

[@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

[@radhekumar3919]

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

[@joisseu]

thank you so much.

[@DraxDestroyed12]

Thank you so much

[@lovelysisters7892]

Good job

[@lucasargandona4658]

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

[@Mesomeone7298]

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

[@Mesomeone7298]

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🤓

[@antoniomele436]

Thank 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

[@baneennabeelaboud8663]

Thank you very good exlpain😎😎😎😎

[@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?