Sequences - Examples showing convergence or divergence

[Goldfishhhhhhhhhh]

Can you make a video demonstrating where a sequence converges towards a value (e.g. 1/2) or something like that?

[patrickJMT]

@Goldfishhhhhhhhhh 5n^2 / (10n^2 + 3n + 4)

[Goldfishhhhhhhhhh]

@patrickJMT i need more videos on sequential continuity and e-delta!!!!

[KidrauhlUK]

@bmdoubleuu .. thats what it ends up as .. like 4! is 4x3x2x1 so (2n-1) will eventually come to a point like (2n-1)(2n-2)(2n-3)(2n-4)....3.­2.1 .. thats what all factorials come to at the end and then they cancel out with factorials on the bottom row if they were any :) .. hope this helps :/

[Heavengirle]

I love you @patrickjmt

[vicb0t]

oh god squeeze theorem again

[zerobeginning]

great help! thank you!

[Machammerballs]

Dumb question, how do you get to the (1)(2)(3) when doing the factorials on the first example.

PS: I'm on chapter 11 of Stewart's Calculus and your videos are a godsend! I thought Calculus 2 was easy and totally made sense, that is until this chapter hit, now up is down, down is up, cats and dogs living together, mass hysteria!

[Machammerballs]

@Machammerballs sorry I mean (3)(2)(1)



[5857612]

you are the best, period

[nightlight12340]

You seriously need to go back to teaching. We need teachers WHO CAN ACTUALLY TEACH.

[patrickJMT]

@nightlight12340 i reach more people using youtube than i ever could boring people in front of a class

[nightlight12340]

You are the only reason why I have an A in Calc II. Bravo. You are fantastic.

[yogabagaba93]

SHOW YOU FACE!

[consumev]

You should put a donate link somewhere

[patrickJMT]

@consumev i have one on my website. click any video and on appears. you should go visit now

[ruttatata]

hey patrickJMT i notice how your videos in general are so helpful and useful than any of my professors' lectures. Quite impressive. What are you? teacher? graduate student? or just a normal guy who loves studying?

[patrickJMT]

@ruttatata been out of school for a long time. taught for a bit. now i am just a guy that makes math videos on youtube cause people seem to like them

[engineerrob1]

You are my hero. I figured this out a few days ago but I couldn't find a video with the squeeze theorem type problem. This confirmed that I was doing it right. So HUGE thanks.

[patrickJMT]

@engineerrob1 happy to help!

[carvallocesar]

How did u get the (3)(2)(1).....

[illestdesimc]

wat about examples where yu have TO USE L'HOPITALS RULEEE!!!! PLZZZ

[mlelope]

Dude, you more useful than my lecturers

[Krooft]

I feel like being a mormon today.

[ArtClash]

6 Teachers disliked this video because Patrick made a lot of students lives simpler.

[pepekong]

Just curious, about how many hours did you study math daily in college?

[chemkokolette]

does a sequence converge only when it approaches 0? What if it approaches a value of say, 4? Would it converge or diverge?

[patrickJMT]

@chemkokolette then it would converge to 4. if you are unsure of these things, look up the definitions.

[InfectedMelody11]

Thank you

[bmdoubleuu]

when youre writing out the factorials, why is it that you have it going off to 3,2,1? i dont understand how it goes from (2n-1) to 3,2,1

[patrickJMT]

@bmdoubleuu well, you are trying to write things generically. for a large n, the value of n! will get multiplied down until at the end you have 3 x 2 x 1. So 100! = 100 x 99 x 98 x .... x 3 x 2 x 1 cause people do not want to write out all 100 factors.

[bmdoubleuu]

@patrickJMT but wouldn't (2n-1) go all the way down to say (2n-9999999)?

[deszczyn]

@patrickJMT You should have said this in the video, if i haven t read this i would be confused myself as to what you did there.

[COEP18]

@patrickJMT But how can it end in like 3x2x1 when it goes upto minus infinity??

[xSnapper26x]

@COEP18 It doesnt go to minus infinity, the series starts at 0 ;)

[newhyperbeamattack]

@bmdoubleuu

Because factorials always multiply itself by a number less than itself, then a number less than that, and so on until it hits 1. So if n is large enough, it will eventually go down to those numbers. Let's say a number x is 10, then it would be: 10*9*........3*2*1

[pjfs80]

@bmdoubleuu factorial n is (n)(n-1)(n-2)... (3)(2)(1), like 7! = (7)(6)(5)(4)(3)(2)(1). I also was a little confused to start with but now it makes sense. Big thanks to Patrick, I have returned to academia after 8 years as a code monkey, and so I am having to get back into math and these videos are a very, very, very big help. I hope I get rich so I can make a huge donation!

[osurulez35]

On the first problem, where does the ending 3*2*1 come from?

[xalexandathegreatx]

@osurulez35 i dun get that either :(

[JoshBuntu]

man i have my calc II midterm in 2 days and I have not gone to class or done homework for 3 months. i know i don't deserve this but patrick i'm going to pass calc II because of you

[MikeldigraSkyStrider]

in the squueze theorem part, how did you get =< 1/(2^n)?

[Elusefelier]

Thank you for this video, Patrick. This really is a new paradigm for learning at your own pace.

[nelmsters]

i thought that if the nth-term test doesn't show divergence, you needed to move on to another test to prove convergence

[patrickJMT]

@nelmsters this is a sequence, not a series.

[sk8tr63]

Yeah your right this whole video is wrong because Patrick did not show convergence at all. he simply showed that they do not diverge.

[ergonomicify]

@sk8tr63 I believe that is the method for proving it...by disproving the opposite.

[cecitsui1989]

how to determine whether converge or diverge??

[wojtek3016]

When you said "mkay" it reminded me of my maths teacher who died few months ago because of cancer. He was really good. Too bad now I got a 60 year old teacher who can't really teach and is just dead boring. Oh well I better get that geometric sequence quetions done for tomorrow. Keep it up man!

[riz222]

Where was this vid. when i needed math? :| GJ

[injury]

anyone know how to determine whether its converging or diverging...i know how to take the limit but im confused after that

[nathanialmunir]

is squeez theorem and sandwitch theorem the same !?

[patrickJMT]

@nathanialmunir yes, they are the same.

[mikeetg]

At 5:21, why does 1/2n = 0?

Thanks, and thanks for all the great videos!

[nathanialmunir]

@mikeetg because there is going to be a biger numer then 2n if you apply the limit

[tomcaputo1]

@mikeetg

As n goes to infinity, 2^n gets larger and larger and gets to a point where you can call it infinity. Now any constant number over infinity is 0.

Think of it as 1/2000000000000000000000000000­0

its basically 0

You can find out by plugging 1/2^n into Y1 in your calculator, go to TBLSET and for INDEPNT. Go to the Table , and plug in 1, 2, 3, 10, 100. At 100, 1/2^100 = .00000000000000000000000000000­8, and anything much bigger than that comes up as an error.

[alleverrr]

this is a peace of cake !!

[patrickJMT]

@alleverrr make cake, not war

[fatqwert200]

@patrickJMT "dont drop the yellow cake!" dave cheppelle show

[patrickJMT]

@fatqwert200 dave chappelle is great

[courage89white]

thank you so much! you helped me out a lot

[r3fuse]

awesome stuff

[FaiththeHairstylist]

Man, I was fine until I saw that Squeeze Theorem. I hate Squeeze Theorem!!! Grr.

[patrickJMT]

@FaiththeHairstylist naaah, it is not bad : )

[othepangel]

Patrick, if you talk about series if the limit is 0 do it converger or diverge? because on your video it converge if the sequence if the limit is zero, hence is it your limit is decreasing?

[patrickJMT]

@othepangel if the limit of the corresponding sequence is zero, it may or may not converge; you still do not know for sure at this point.

[othepangel]

Patrick, if you talk about series if the limit is 0 do it converger or diverge? because on your video it converge if the sequence if the limit is zero, hence is it your limit is decreasing?

[Maxielleatsbabies]

wasn't it cos^3(n)?

[karlitosky24]

When i was in the point to get frustrated for my test tomorrow i found ur videos! u're a beast dude!!! students are better than teacher...

[karlitosky24]

When i was in the point to get frustrated for my test tomorrow i found ur videos! u're a beast dude!!! students are better than teacher...

[kingstun]

dude that was great i was totally with you up until you drew a phallic symbol at 5:36

[football5770]

really helpful, have a test in Calc 2 tomorrow.

This really clears things up, since my teacher only spent a day on sequences.

[geovaniluna]

Thank you ! (factorial).....

I promised once I graduated and I got a job I'll donate to your website..

[mzhannah11]

can you number your videos by sections or at least have some organization to it so im not scrambling everywhere to look for them :) thanks!!

[reubinsidhu]

you are god...

[68hinduhammers]

so if you take the limit and it is 0 is convergence and if it is a constant it is divergent

[ossian1977]

left handed! must be the Leonardo genius trait ;)

Cool vid.

[thegambitking]

I'm left-handed too, but I smudge the page a WHOLE lot more when I write. You're an inspiration!

[pitaguesmk]

You are a great teacher :)

[scarykidbryan]

saved my life man. i would have failed my test if it wasn't for this vid

[P5videos]

i agree...you explain much clearer than even my class teacher...

[francoantonio63]

Not a hater or anything, just an honest question. You are currently using the general divergence criteria. But doesnt that just proves divergence? Harmonic series terms tend to 0, but it stills diverges. Im kinda confused.. good work on these vids btw! keep it up!

[indianboy603]

Yes, I agree with you

the nth term test (lim as n->infinity) only proves if the function diverges nothing to do w/ convergence

[ak47m16]

@francoantonio63 yea i dont understand why it diverges there either..

[diegoramos27]

What happens if the limit is different than 0 ? Is it the same than series, the sequence would diverge if the limit is different than 0 ?

[mikes92089]

I gotta thank you for your videos! I had to missed my calculus class for 2 weeks and didn't know what was going on when it came to turning in the homework. About a week before the exam, I started watching your videos, and I was surprised on my exam grade. I got an 85 where the class average was a 70. The only thing that I didn't like was that I missed the easy problems by doing careless mistakes. I like to thank you again. You're the best!!!

[JamesBondOO]

thanks for the awesome vid.

just wish i found this at the beginning of the semester :D

i still have the final left so :) thanks a lot for this and all the other vids.

[diagonir]

Extremely clear, thanks much!

[Loka72707]

thank u so much for ur videos. i being having some problems in my calculus class but the way u explain things make it soooooo much easier. again thanks :D

[TheValmont1956]

I came upon these videos by accident. I actually know Patrick personally. He IS a calculus teacher and an exceptional Tutor. If you are in the Austin area you would really benefit from his help and should go to his website. I took his class for pre calc and felt really well prepared for calculus.

Ian J Valmont

[whomuenvy]

THANK YOU SO MUCH! Please keep these videos coming. They are really helpful!

[lefty1042]

You would make an excellent teacher... You explain it much more clearly than my calc professor. Thanks so much for the video.

[HeresSeem]

great job, keep it up dude.

[OutrageousElephant]

the limit of cos^2n/2^n was on my last test. Patrick ftw

[PHILANTHROPIST1988]

GREAT JOB 5*

[opeth1234]

finally something useful on youtube...

[pqvnzla]

Hi, i was wondering if you could do an example involving a ln? it's confusing me hehe

[ExecutiveMarco]

nerd XD joking

[dagiffy]

You are better than most PhD instructors I know. You can actually teach, and that's far more valuable than any piece of paper smeared with ink.

[jrockxblood]

Thank you sooo much for this vid. I have a math test today and sequences are likely to be on it, and I didn't do well with them before, so this helped a lot!

[Bodacious1966]

Patrick, could you explain why you ended the sequence with 3*2*1? Is this just the very last part of the factorial already expanded for the very last term of "infinity?" Apparently I'm not the only one who got a little lost by that. Thanks bunches.

[patrickJMT]

yes, i always end with ....*3*2*1 as the end of a 'generic' factorial expanded out.

that is the trick with factorials: expand and cancel

[stillmybleedingheart]

Thanks so much for these videos, my textbook is terrible at explaining series and sequences and these are helping a lot...

[Luciana08E]

Could you make a video about Bounded and Monotonic Sequences? I think I would know how to determine those with a graphic calculator, but I'm not sure how to do this without one.

Thank you sooo much for your videos, they're all amazing!

[Koogea]

ooo ok thanks

thanks again for doing these videos, they have helped me a lot throughout my highschool and university

when I start earning money I'll send you a check : D

[Koogea]

so you used test the series with the test for divergence but how come you conclude that the series converges since this test only tell us that if lim -> infinity of an = 0 then the series may or may not converge.... am I right or wrong I just what to know

[Koogea]

by the way can you please do (if you ever read this message) series starting at 1 going to infinity of xlnx/(x+1)^3

thanx!!

[calctmnt]

why does the sequence go to 3x2x1?

[danaleslie]

(2n-1)! -> let n = 3 -> (2(3)-1)! = 5! = 5x4x3x2x1

when n=infinity there are an infinite amount of terms in the factorial expansion, he just uses ... 3x2x1 to represent the end of the expansion.

[xylokid4]

lol i still don't get it

[agnes213]

this was pretty helpful but I was wondering if you could post more examples of the sequence and series problems!

ps- i managed to get a B+ last semester because of you =) thanks a lot =)

[ksater2]

thanks a lot patrick... a big help.

[scientificboysclub]

wow squeeze theorem or sandwich theorem !!

[scientificboysclub]

wow thanks for help !!

[cracknigga]

dude, you're greater that jesus!

you're continuing to save my ass and i don't even have to get up early on sundays for this

awesome!

greets from russia

[Trestkon]

Wow, fantastically informative video!

[brilliantfranz]

Patrick have u thought of making some multivariable calculus stuff ???

[patrickJMT]

i have a bit of it up there... but i could do more!

[264350422wil]

hey patrick, for your first example, lim n>infinity of An goes to 0. Doesn't that mean it can converge or diverge? because u saw your video about test ofr divergence and geometric series. O.O

[patrickJMT]

you are getting sequences and series confused i think! in this video, i am talking about sequences!

[brilliantfranz]

you have no idea how great is to watch your vids....

One of the many things I like about your vids, is that you put your things in perspective... i mean, you show how everything in calculus in related to everything in calculus, and show us there us no reason to learn things like a robot... but knowing where things have its origin

Cheers from Venezuela

(Sorry if it sounds funny, my english is not that well)

[patrickJMT]

thanks friend, i am glad that i have been able to help you

[shiv86]

thanks! theres such a big difference between teachers (especially in maths) who simply show of their knowledge compared to teacher who actually want to teach their knowledge ....thanks for the vid :)

[patrickJMT]

happy to help : )

[69adrummer]

Killer video! Nice handwriting, nicely spoken, well done. I could not, however, avoid getting goosebumps as I imagined the sound of that sharpie hitting the paper! *squeak* *squeak* lol, details!

[jrumpi]

hey patrick i have a problem in bounded sequences , how do i know if its bounded and how do i bound it, i mean what are the steps . i hope u can help me because this thing is making me a big problem .

[microsoftkof]

這種題目可以用Mathematica這套軟體去執行

只要1sec就可完成

[Bonartist]

Nice one

[Dorenimenimynimo]

You are wonderful, you just saved me...there is light at the end of the tunnel/calc II class.

[Kmwiti]

thanks a lot, i'm doing calculus 2 right now and I think you're great teacher.

[patrickJMT]

i try!! : )

[03IMPALASS]

hey patrick why did you put (3)(2)(1) in the numerator and denomenator...i dont get it!?!

[rigaude]

Thanks for the help!

[patrickJMT]

no problem!

[erithug]

lool r u guys going to mcmaster engineerin

[skaterceo]

do you get your problems for a textbook called

Calculus: Early Transcendentals

??

[patrickJMT]

yep! most of my problems come from james stewarts calculus text book! 5th edition i think

[DMAlivenow]

Haha thats what we are using for calc 2

[patrickJMT]

yep, popular book... his and larsons

[ViadoMundo]

AMAZING! I'm watching most of your videos and... WOW You great! Thanks a lot!

[patrickJMT]

thanks! glad they are helping

[brco2003]

i have never seen this topic explained so clearly thanks!

[patrickJMT]

thanks!!

[CiaranW]

Very helpful, thanks

[alhino]

superb mate i needed this badly

[matador0731]

thank you patrick and thank you for share your knowledge with us .

[patrickJMT]

my pleasure my friend! i hope the videos help!

[matador0731]

how do you cancell out 2n-3 in the numerator from example 1...IF there is no 2n-3 in the denominator.

[patrickJMT]

but there is a (2n-3) in the denominator... i just do not write out all the factors

[matador0731]

very clear