Absolute Convergence, Conditional Convergence and Divergence

[redrum41987]

Doesn't the Alt. series test say they all have to be positive?

[LordSeptios]

At 1:28 I was about to scream out my typical classroom "WAIT don't erase that yet!" But then I remembered the amazingness of online lectures and rewind power.

[StL33T]

In your second example you have 1 to the power of n+1, where the upper limit of your sum is infinity - to which you canceled out. But isn't it true that 1^infinity is not 1, but actually an indeterminate number? Then what?

[etiennez0r]

Thanks bra.

[ashrayrs]

4 maths teachers disliked this because their student are studying here rather than in their class

[Jumpman0818]

@ashrayrs I'm an IT student, year 1 ; and I learned 600 times as much Analysis from this page than from my "professors shouldn't teach" professor

[seaweedsupper]

In the last example using the test for divergence, don't you have to take the (-1)^n into account? I was under the impression that the only time you can ignore it is when doing the alternating series test...?

[blobothy]

sooooo helpful in my calc c midterm review. thanks a bunch!!!

[SSpitz16]

can we only do this if it is an alternating serie?

[MustangGTR2]

dont get mad ,but WHAT IS THE USE OF THIS ?

[patrickJMT]

@MustangGTR2 it gets used in differential equations, which is hugely important in physics, for example.

[StormHammy]

@MustangGTR2 For Science!~ ^(O.O)^

[iCashuu]

If the absolute series equals 1 but the series is convergent using other tests, would the series be considered conditionally convergent?

[Syboltleffert]

Great! Thank you

[pimpmymail]

Then Patrick, you are Absolutely Convergent, ( where Convergent = Awesome ) !!!

[5otrebor5]

Can the sum of a series (a_n) converge absolutely if all (a_n) are negative?

[patrickJMT]

@5otrebor5 yes

[o4nsb]

Sir PatrickJMT!

[11m0]

Absolute convergence is to go even further beyond!!

[meedan1]

god bless you

[joeratti]

just letting you know this lesson comes before the ratio test lesson in many of the text books ive seen

[Fg5x3]

I wish I had saw this a few weeks ago

[bodinian]

Initiate religious argument:

This video is a lie! You can't prove any of this is true. Calculus is just a theory, I never say a logarithm in real life and the Bible never mentions it so it must all be man made to keep us away from Jesus. Don't fall for the Devils lies! Repent Nao!

[bodinian]

@bodinian saw*

[Richardhuang70]

for example 3, could you use the alternating series test to show that lim n-> infinity of n/(n+5) = 1, and that n/(n+5) does not decay monotonically to zero, therefore the series diverges?

thanks =)

[TheDdealwis]

@Richardhuang70 wassup richard? emily misses you

[Slycooper2456]

Wow your doing my Hwk thanks!!! and it helped solved the rest so thank you very mcuh

[yogabagaba93]

@Slycooper2456 cheeky mungral

[zz904zz]

A billion videos later, I finally realize he's left handed haha.

[alrasw]

i love you!! Sharing your knowledge so freely and politely...God bless you!

[phalanxYgEnsem]

thank youuuuuuuu.... i almost failing cal2 ... you help me a lot....

[toadexleen]

Woah, HD......

[VinzVT]

Great work, really helping me get prepared and confident for my finals

[mdrodsuwan]

you're a leftie. hahah great people

[Bugga951]

@xcaliberpeng Your comment helped

[aloich39]

very clear explanation.

[qaylin]

Seriously man.. Im in calc2 summer classes and we get 1.5 weeks to go over series. You're a huge help.

[TheIncredibleOwl]

I fucking hate these commercials! Honestly NO ONE GIVES A FUCK!. were mostly here because we want to know how to find Abs Convergence.

[Amit93]

3 people diverged

[wellitstrue102]

1:42 FAIL.

i like the paper & sharpie videos better

[monik925]

u are the bestttt u totally saved my lifee I have an exam 2morrow and I understood thanks to youuu!

[hourmat1991]

what's 2 plus 2?

[stephenxluo]

@hourmat1991

6.74

[starlight277]

I wish you were my calc teacher!

[evnouski]

Okay, I've decided that I'm going to hunt you down and give you a hug! (non gay buy the way). Your videos are amazing! Thank you so much!

[AfghanPathanWarrior]

3 people failed to click the like button or took a test on absolute/conditional convergence and divergence before watching this video. :)

[yucky1336]

patrick in the second example you showed that it was divergent because the limit was one. why did you try to show it was conditionally divergent. i dont get it.

[pinktennischick]

calculus final exam tmrw. i was so scared but your videos have been a big help. they are so well explained, and easy to understand. and you have legible handwriting too! :) thank you so much for saving my life :)

[talflick]

one little piece of advice for you, just housekeeping, really, is to move the p-series videos BEFORE all the convergence tests, since you reference p-series before you explain them. it would clear a lot of things up for people like me watching this playlist from start to finish. :)

[ThisComputerGirl]

thank you soooooooooo much. my teacher rushed through this on the last day so I didn't understand any of it. and half of my test is on this and my test is 80% of my grade. eeeek. Hope I do well.

[MrBrandonthegiant]

handwriting.... so... perfect.....

[patrickJMT]

@MrBrandonthegiant tryin' to keep it neat for all you people out there

[titan59]

my professor is so jealous he cant teach like, he went to all your videos and disliked them. . .

[Blu3sKLUZ]

I LOVE YOU!!...but no homo. lol

[Esco481]

Thanks Patrick this really helps! I tried reading the textbook, but it was just simply too confusing.

[Robbinizer]

good stuff

[JaoquinQ]

Do you record this with a document camera?

[JaktheAtheist]

I wish my sigmas looked as cool as yours >_>

[belachewhm]

Dude, you're awesome. i've been watching you since i first learned calculus in high school, and you've never failed me yet. Keep up the awesome job!!!

:D

[meetyourfate192]

So does conditional convergence basically mean the convergence or divergence for the absolute value of the function and the regular function are different? Does it matter which one of the two is convergent or divergent? The way you explained it it seems like it ONLY will occur when (an) converges and |(an)| diverges, not the other way around.

[angelprincess12345]

patrick jmt is like my savior for calculus

[iniloy1993]

Dude ur amazing...can i rape the "like button"??

[patrickJMT]

@iniloy1993 you do whatever you feel is necessary with your like button : )

[yogabagaba93]

@iniloy1993 dont use rape inappropriately

[patrickJMT]

@xcaliberpeng it is inconclusive

[bnduong9132]

Love how you do examples that are a bit challenging unlike the usual simple book examples

[YomotokeDash]

Great video! Thanks a lot. Really helps a lot :)

[buckfan89]

Please continue to do this. It has helped me to understand calc 2 far better than any of my professors so far. Thanks again for the videos

[mshiraa]

How come you didn't use the alternating series test when you were trying to find if the series was conditionally convergent in 10:02?

[makuta204]

@mshiraa b/c the equation alternates between +1 and -1. It doesn't fit the requirements that equation (b sub n ) is eventually decreasing. Technically it is diverging, (that's what you would put on the paper if this came up) but the real answer is it doesn't exist, because you don't know what your final value is, since infinity is neither odd or even.

[myez]

Love your videos, Patrick. Have you ever gotten light headed from using sharpies and whiteboard markers so much? I start getting light headed after writing with a sharpie for a few minutes.

[PolarisUSMC]

Khan Academy is pretty good, but I really do like that you work with more difficult problems. It really makes life easier and easier to understand.

Do you teach at all or is this just for fun?

[patrickJMT]

@PolarisUSMC i used to teach in a classroom. i still take 'private students' (that is, i do a bit of tutoring). however, i do enjoy making the videos and chatting with random people out there on the internets, so it is also 'for fun'

[embraceforever21]

Once again, you have saved my grade :)

[amcbirds]

hey shouldn't you ignore the (-1)^n part when ur finding the limit for last problem???? that way you get limit =1 which is not 0, and therefore diverges?????????

[sale3sale]

Thank's!!! You're the best! :)

[hurricanes102191]

All three examples were the first three odd numbers in my book. This guys my hero!

[LolixxDollie]

I hope you do calc 3!

When I get my scholarship money I will DEF! donate some (because right now I am a poor college student)

[jvideogamer]

I have a question on my homework that asks me the determine whether the series converges or diverges and if it converges to find the sum. The question is a series from n=1 to infinity of (4^n)/(e^(2n)). I could really use some help, i dont even know where to begin!

[patrickJMT]

@jvideogamer it is a geometric series; just rewrite so that it is all being raised to the n power, determine if the ratio is less than one (and greater than negative one)

[n4his22]

Really these are very benficial videos.I would like to ask you if you support some examples for uniform convergence or even send us a good reference for solved problems of uniform convergence.Thank you a lot.

[n4his22]

Really these are very benficial videos.I would like to ask you if you support some examples for uniform convergence or even send us a good reference for solved problems of uniform convergence.Thank you a lot

[alrasw]

patrick i'd buy u an eraser for ur white board...only prob i live in the Caribbean...lol

[Artopunk14]

Thanks for the help.

[alexistequiere]

I may just pass calc II because of you.

[gsowx2]

For the conditionally convergent test for problem 2 and 3, you said on 2, that its an alternating series, so you ignore the alternating part (-1)^n+1, but why didn't you ignore it for 3?

[260191894]

I finished with an A in calculus 2 thanks to your videos! They are clear, concise and straight to the point. Professors mix up their students by giving to much information that will not be applied by the students in their career (e.g. as chemistry student, I need to know how to use calculus, not prove theorems).

[patrickJMT]

@260191894 but math majors in your class do need to know how to prove theorems, and they are not gonna hear it in chemistry class : )

glad you like the videos!

[260191894]

@patrickJMT I know... but I wish science students would have specialized calculus courses like engineering students: they basically learn how to apply. Still, thank you very much for your videos!!!

[123Retry123]

These videos are a life saver, thank you so much!

One question tho. Why is it that as soon as the ratio test says it's convergent, it becomes absolutely convergent? For the other alternating series we had to prove that it was also decreasing, but this one we don't?

[patrickJMT]

@123Retry123 well, the ratio test uses absolute value so you are testing for absolute convergence at that point

[123Retry123]

@patrickJMT Hahaha oups! Thanks! Didn't think of that

[greyfoxxelite]

Your videos are amazing keep it up!

[aynwoodward]

this is so helpful (especially b/c my final is tomorrow)...thank you! 

[newfella1]

This was so hopeful thank you so much!

[ayamfuckingdead]

Ha, cool thing you hang around in Austin, my friend is going to study there this fall! (We are from Sweden.) Your videos are really really great. Thank you so much!

[patrickJMT]

@ayamfuckingdead ha sweet!! tell him/her to come give me a big HIGH FIVE if they see me in the FAC

[hannahhutyra]

i LIVE in the FAC, maybe i can give you a high five as well!

[patrickJMT]

@hannahhutyra that sounds sweet! i was there yesterday and will be there tomorrow as well : ) look for the left handed guy with the blue bandana - that is probably me : )

[1Blindguardian1]

you should really consider returning to teaching! specifically to university of south florida in tampa lol!!! we need an outstanding professor such as yourself.

[patrickJMT]

@1Blindguardian1 ha, thanks for the idea, but i am quite happy in austin : )

just keep watching the videos til i get bored and end up being a beach bum!

[shasanni]

@patrickJMT patrick is austin really as weird as ppl say it is =)

[Sumitalianguy6]

very helpful!!

[bishops1queen]

dude. my test is in an hour. this is actually clearing it up for me!

effing awesome!

[Cerebrob]

Great stuff! Really helped for my AP studying.

[tyeedillon]

save my life

thanks

[VWinUgo]

u rock thanks!

[HarukaNUsagi]

Subscribed. I'm taking Calculus II this semester and I'm a non-traditional student. I may or may not major in math. I have been referencing your videos for the past year or so. Thanks for uploading.

[meiskann]

i'm probably going to end up watching all of your videos before my final exam.

thank you so much!

[rararaRACHEL]

i may not fail my test tomorrow.

(technically today.)

thank you so much.

[lifematch]

his example are right off from the multivariable calculus 6th edition text book. lol. not that i am sayig that's bad but found it suprising since i was watching this video while doing my homework.

[indianboy603]

thank you so much!

[TheCriticalGouge]

Very Nice!

[diegoramos27]

The world wouldn't be the same without you!

[whomuenvy]

You have helped me sooo much in Calc 2 and Calc 3. Keep up the good work! Keep those videos coming!!

[lilbarlet]

How do you know when to ommit the (-1)^n when taking the limit and when to include it? Im a little condused on that.

Btw your videos are amazing as everyone else says! Thank you so much. Too bad you don't teach Chemistry too. :)

[picsmics4]

Patrick JMT I'm in absolute love with you

[atran12]

which video do you show how to simplify factorals? btw, you're videos are so invaluable!

[deanusbeavo]

thanks for the help, come take my professors job please

[hmthmhh]

you cannot just plug in numbers to prove that the series is decreasing. it could diverge at first but what if it increases later on?

[RearEntry295]

I think I am in love with you.

[vanessa2218]

God Bless you.

[IsabelleD88]

You made it look so easy, and quite frankly, it is... I finally get it, thanks! :-) This makes more sense than my thick Calculus book..

[dudeitskumar]

makes a lot of sense...thx for teh help

[RadoAller]

ur awesome man!!!

[5tones]

thank you that was helpfull

[bloodydonny2009]

good stuff man! all the way from australia, first year engineering maths has never been easier, i havent showed up to a single math lecture this semester since i found your videos!

[xylokid4]

Another jumble of stuff to remember....man sometimes I feel like Cal 2 is just vast amounts of memorization!

[daniel4melissa]

nuff respect for making des videos, im sure alot of maths students will benefit greatly. keep doin ur ting!

[Poke4Poker]

nice arm hair!

[patrickJMT]

thank you.

i am very virile

[jm30603]

Great addition to the Series videos! I totally get it now!

[jimen113]

I love your videos!!!!

[vampire9966]

In fact, the Gregory series pi/4 = 1-1/3+1/5-1/7+...... is conditionally convergent too. Do you know why? :)

[patrickJMT]

yes

[27istheNumber]

hahaha

[Waranle]

Thank you Patrick :) good stuff

[peiznkev000]

Oh wow...If only I saw this 24 hours ago I might not have bombed that test....

:(

[jiamonx2]

@peiznkev000 omfg same shit, i missed this video and I took my test 10/40

[21chuck]

yea youre pretty incredible this was just my hw tonight

[LqFFREAKK]

omg we're just learning this now

your amazing!!

[pollardrho06]

Good Job!

[badger15x]

this stuff gave me a lot of trouble, but u cleared a lot of it up. thanks!