What is a Series

[dajakesta1234]

hey patrick what do you call a sequence that has a property of a2-a1=a3-a2

and a2/a1=a3/a2 please tell me

[welk0metohell]

Learn more on youtube than coming to class. Feels weird for paying tuition!

[patrickJMT]

@welk0metohell you can make a donation on my website if that feels less weird ; )

[da1booger13]

@patrickJMT

Hahah, your remarks always make me laugh Pat. Mind if I call you Pat? I've been watching your vids for so long that It just feels that comfortable.

[omoragan]

the hairy arms of calculus gives us great knowledge

[osvideosdojoao]

I saw the first 8 minutes, and it seems like sequences. I'm in secondary level (calculus I ), soo I still not learn series.But good explanation!

From Portugal

[emsta13]

Why can't everyone make concepts this clear and concise? YOU ARE MY HERO.

[wizardval]

thanks for everything bro. you rock. I'll donate more money to you!

[systemnate]

Great video. Thanks a lot! Just wanted to say that in addition to the limit not equaling zero, if lim as n-> infinity does not exist, then the limit will diverge. (i.e. (-1)^(n-1) ).

[sano0311]

at 7:39 you have "a/1-n" shouldn't it be "a/n-1" because when you plug in "n" values in "a/1-n" you would get negative numbers. Am I wrong?

[sano0311]

these stupid commercials :(

[MeSooCrazyy]

Why do all maths geniuses are left handed ??lol

[tryceo]

Wednesday is the AP CALC BC test... Good luck everyone!

[wierdo5000]

i love your sigma notation.... it owns. 

[kornsux10]

Smart ass, I wish I had your brain for calculus AP test!

[squisheebananas]

Does the Test of Divergence apply to the Geometric Series? I'm just a little bit confused because the Geometric series goes to a number that is not zero (10/9) but it converges.

[deszczyn]

@squisheebananas the series goes to a a number non zero(10/9). But the limit of the SEQUENCE goes to 0. (therefore you take the limit of the function not the series)

[squisheebananas]

Your videos are the best. I'm a little bit in love with you.

[lemonader6]

PatrickJMT is the man

[trickoff]

You are a God at explaining! Why do we need books when we have you?

[kwhitley125]

if it wasnt for this guy, i woudve probly shot myself by now from all my bad math grades

[Drake8604]

I'm kind of dreading Cal 2 next semester after watching this vid. I'm in Cal 1 this semester and I thought it was pretty easy, but I'm not getting series so far. I think I just need to review summation a little. Thanks for the videos!

[Oblisk47]

PatrickJMT for president 

[Tripleclaw1]

UTBMat 1120: Geometric Calculus II with YouTube. That would be my dream class.

[madgt95]

Thanks wish me good on my test :-)

[patrickJMT]

@madgt95 good luck!

[anvar011]

@patrickJMT Hi dude. I need some help with series like T=a^1+a^2+a^3+...+a^n. Can you define T in terms of 'a' and 'n' like in the case of 1+2+3+...+n=n(n+1)/2? I've been puzzling over but still can not formulate it.sorry for my bad english.

[Q8RedDevil91]

you just made me understand something i thought it was impossible for me to get it !!!!!!!! :-o

[ldahir]

thank you soo much, your vedios are soo helpfulll, i dont know what to do without them

[RefaelBA10]

Thanks for the video. I have a test tomorrow and it's a great review of everything I learned in the past few days, just chilling out and watching this great summary.

[AmaymonF]

You should be my math professor at my university lol

[Parro32091]

great video... i learned more in 12 minutes than i did in 4 college lectures haha

[LolixxDollie]

@Parro32091 Agreed

[PeeteyP]

5:40 onward is the meat of the act.

[ActorGuy]

Patrick....love your work. If I could make one suggestion it would be to maybe group these Sequences and Series videos in the typical order given in say either Stewart or Thomas. I'm in Calc II and I'm just sort of figuring out which to do first. But my prof has been mixing everything up for two terms now anyway. LOL.

Which text do you base your examples on? We are using Thomas 11th Edition.

[patrickJMT]

@ActorGuy yes, yes. everyone wants a playlist. they are just very very very tedious to maintain, but i will get around to it. i just hate tedious things so much.

[ActorGuy]

@patrickJMT Understood...tedium is a pita for sure. Great stuff on the Calc 3 videos as well. Looks like Linear Algebra for me next term.

[teluguc]

@patrickJMT lol not to be an ass but there are still no playlists and its somewhat difficult to find vidoes, cuz i am sure i missed some. please get to it and keep up the great work!!

[patrickJMT]

@teluguc uh, there are playlists for calc 1, calc 2, and calc 3 on my channel. not to mention that i also organized all the calculus videos on my website and put them in sequential order...

[yadeniky]

@teluguc you can always go to your book and look up what you're studying, then search for that specific topic

[patrickJMT]

@yadeniky that would make too much sense to do ....

[ynut666]

@ActorGuy that is a horrible book, stewart is much better but still a crap :)

Youtube is the best :)

[ActorGuy]

@ynut666 So true...but we just changed textbooks at the beginning of the year...starting with the Calc 3 sections. We are now on Brigg's and Cochran's Calculus, Early Transcendentals. Frankly, it is the best text I've seen so far. And I'm sitting on copies of Stewart and Thomas.

Check that one out if you can. I find it readable and pretty complete. Of course what helps is actually understanding the theorems, definitions and proofs,etc. But yeah, a great book. IMHO :)

[MaraimH]

you're amazing :)

[phoLegit]

isnt there a formula for infinite series?

where it is a / (1-r)

where a is the first number and r is the common ratio

[patrickJMT]

@phoLegit this formula works only for geometric series where -1 < r < 1

[dizbjade]

@phoLegit Immature moment, but sorry, but you just got OWNEDD by PatrickJMT! haha

[phoLegit]

@dizbjade lol? 5 months ago, dam. anyways I wasn't stating him or doubting, I was just asking since my teacher taught us that way and I wanted to clarify if it.

[thehotsteal]

hi

can you do a video for complicated problems

[baglady999999999]

yo man youre a monster beast at math

[patrickJMT]

@baglady999999999 only requirement: many thoughtful hours

[HoloUniverse]

Thank you very much!

[beennz1]

you have saved my life

[cervantespr]

Todas las series alternates divergen? se me olvido... heheheh

[silhavydan]

great!

[Nanumir]

very helpful, thanks a bunch

[utheather]

Dude these videos are the best calc videos I've found!! (And I've gone through quite a few. heh.)

[scrambledxeggs]

thanks! this was very helpful!

just wondering dont the markers smell a lot?

[granadaza]

Way to go Patrick! Thanks

[KingScar06]

Oh nvm, it should be (-1, 1), sorry.

[polzowatel]

ops my bet, same thing))

[patrickJMT]

only if both are positive : )

otherwise -3/1 would not work (negative 3 is less than one)

[polzowatel]

isn't it 0<|x|<1 ?

[christopherchubb]

an absolute is greater than 0 by definition, its superfluous and unnecassary

[RylyC]

The zero doesn't need to be written.

[masterncomder23]

I'm taking Calc BC this year, and we went over Series and Sequences and it was pretty confusing. So, this was a pretty good review.

[masterncomder23]

Excellent Calculus video, Patrick. Really informative.

[dezihunk]

Thanks A lot!

My Instructor this quarter for Calc 3 just copies examples done in the textbook & reads the text. Looking at these videos make sense now! Thanks yet again!

[Kimidoki]

thank god i finally found this video ;_;

all the other videos either glanced over it or it was hard to understand.

thank you very much i have a sequence and series test tomorrow!

[abenebaby]

you are amazing! thanks so much! i was so confused with series

[lalolita5]

Patrick, how do you do this:

Sum (n=1 to infinity) of arctan n ????

I could not find anything similar in your videos. The squeeze theorem maybe? or not at all?? Any guidance?? Please please!! :)

[patrickJMT]

use test for divergence

limit as n goes to infinity of arctan is pi/2, so the series diverges!!

[vadskjld]

very Usefull .. Thanks man :)

[kudakadere]

i'v tried to come up with the series for prime numbers but i'v had no luck so far. can u help me

[patrickJMT]

not sure what you mean...

[kudakadere]

usually if there is a sequence of numbers you can find a general rule for working out the next number if you know the previous number. i tried to do this for prime numbers but it seems really hard.

[gBakos126]

I'm pretty sure it's impossible to do this. I watched an episode of the show "NUMB3RS" and they were trying to do this.

I got this from the show:

If someone would work this out it would be a disaster, because internet encryption relies on prime numbers to encode private data on the internet. Prime numbers occur randomly on the number line without order.

[patrickJMT]

very true: prime numbers play the key role in encrypting data

[ToniHTChen]

awesome ^^*

[patrickJMT]

thanks!

[619kammy]

Can you do a video with arithmatic or geomatric sequences when for example you know a14=56 a21=67 and you have to find the nth term or a1 or a65.

[ViadoMundo]

Hi Patrick! :)) Nice video, watched it in google videos :)