Using the Ratio Test to Determine if a Series Converges #2

[melisantika]

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[Onepissite]

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[Ondelendo]

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[bebeheuy]

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[willamricard]

Nice Video That You Share , So Very Nice Thanks You Using the Ratio Test to Determine if a Series Converges #2 - Two more examples are shown using the Ratio Test.

[imegatrone]

I Really Like The Video Using the Ratio Test to Determine if a Series Converges #2 - Two more examples are shown using the Ratio Test From Your

[classicrocker258]

For the first example would it be easier to use the ratio test or the root test?

[meedan1]

it is convergent, fine. But why absolute convergent? pleeease reply!

[myketheoneill]

What if there is 1/(2n)! ? How do you cancel out and set up that problem to determine it is convergent?

[Eaturveggies21]

My teacher made us a study guide with about 20 series problems and over half of them were examples from your videos.....which is cool, but she didn't even mention you!!!!!

[daemonpacman]

Here's a testament to how good of a teacher you are:

Throughout this whole video, the only thing that confused me was how you can write with a sharpie without it bleeding through to the next paper. HELP! I have a test on this next Friday. ;3

[patrickJMT]

@daemonpacman ha, good luck! there is a sequence and series playlist with lots of stuff. you may also check out the videos on the right side (related videos) as some are missing from the playlist.

[lorijoy720]

You might be the reason I pass calc 2, hahaha D:

[aloskingdom23]

your a gift to all math students Pat

[arodri49]

These videos are amazing study helps. I go to MIT and I find your videos more helpful than MIT's own videos.

[Tannerhasabike]

patrick you have saved my life , thank you so much

[1ordofsarcasm]

I'm a little confused about why ((n+1)/n)^n is e-but then again I'm really confused about e and the natural log in general-do you have any videos or other resources I could use to help? Thanks! :)

[1ordofsarcasm]

Thank you!!!!!!

[truBob91]

but he could have used the root test for the first example......that was easier

[TheGame420Hurricane]

You sir are amazing!

[mattazio]

For your last example, the one where you said that because the power of the bottom is greater than the power of the top the limit would be equal to 0, wouldn't it be considered divergent if you used the p-series in the end? If the problem was, perhaps, (n^2 + 2) / (n^3 +1), and if we were to take the limit, that rule that you stated wouldn't apply because the p-series would prove it to be divergent by comparison theorem.

[vampiracy]

@mattazio

When we do the ratio, we're no longer working with the same function. The properties of our ratio is different from the original series and therefor different conclusions need to be made. You're right that the ratio would be divergent, proven by p-series. However, we aren't looking to see if the ratio is convergent or divergent, but whether it tends towards a number less than, greater than, or equal to 1 as it goes to infinity. This tells you if it converges or not.

[vampiracy]

@mattazio

A good analogy would be a function and it's derivative. If we're looking for a min/max on f(x), we would be looking at the zeros of f'(x). We will likely find that the zero of the derivative is not a min/max on the original function, because we performed an operation (differentiation) which fundamentally changed our function and it's properties. This is similar to the series-ratio relationship because we performed an operation (division) on the series which fundamentally changes it.

[vampiracy]

@mattazio

"We will likely find that the zero of the derivative is not a min/max on the original function"

this is meant to be "not a min/max on the derivative"

[almass281]

THANK YOU SOOO MUCH MAN ... I REALLY APPRECIATE WHAT YOUR DOING ... THANKS AGAIN :D

[iloveu157]

THANK YOU

[tmac1ninja]

you should win the nobel peace prize!

[patrickJMT]

@tmac1ninja i wonder if the chinese would put everyone under house arrest and not let me go

[ProkofievRules]

Great stuff. I was never actually taught this stuff in my last school, in a program designed to transfer to my current school. Now, in differential equations, an entire chapter is taught on using Power series to solve differential equations. These videos are great, as they bring me up to speed on what I need to know.

[Ayplus]

Great video once again. Lol i remember the first time i saw a factorial i was like why are these numbers so excited. . .:S

[liverpool852]

U R great professor

[1SockPants]

this is awesome. 

[kakaboo]

Hi

I do not get why limit->infinity [(n+1)/n]^n is e^1???! shouldn't it be 1 or infinity????

[patrickJMT]

@kakaboo nope; 1 ^ (infinity) is an indeterminate power; you can use l'hospital's rule to find its value. in this case, it is e.

[kakaboo]

@patrickJMT do you mean that limit->infinity [(n+1)/n]^n = 1^(infinity) = e?

or do I just apply L'hopital rule directly to limit->infinity [(n+1)/n]^n? even so, I dont see or get where the e would come from....

[lano1106]

@patrickJMT I check my calculus book and you are right about 1^inf being an indeterminate power. My question is why? What is the proof?

If you do 1^(10^1000) = 1 or any big exponent value the result is going to be 1. Why is it different with inf? Do you have a link on a document explaining this? Thank you,

Olivier

[kingstun]

HOW COULD SOO MUCH GOD GIVEN TALENT BE CONCENTRATED IN ONE PERSON?????im just hatin. Seriously you have a gift to break very difficult concepts down into easily understandable material.

[patrickJMT]

@kingstun ha well, it did not just magically happen. i worked my ASS OFF in school.

[amrty1]

@patrickJMT hahahahahaaha

[fuckinpete]

i love you. I have an exam tomorrow and was just about to give up on revision before someone told me about your page. Now I finally understand maths again. I'm not more confident going into this exam than I have been for any exam in the last 2 years. Thankyou. I'm telling all my friends forsure.

[patrickJMT]

@fuckinpete glad it helped!

[bryanliau]

Thank you Patrick!!!~your video help me finished my assignment!!!

[warnick80]

lectuers r rubbish at describing this stuff but ur vidoes helped me alot =]

cheers man

ur videos r awweesome

u r a legend

[CrazyIemon]

Wow, you're the Paul Hewitt of Math! Thanks for the video!

[Frankreif]

not that it matters, but you could have cancelled once more on the last example:

(n+1)^2 / (n+1) = n+1. It was just blindingly obvious I had to comment. :) . Nice tutorial though.

[xvillalon1]

You always tell us "secrets" I feel like my proff does't tell. Should get an A with your help!

[yumyum210]

thanks a lot, great help, feeling pretty confident of at least a four thanks to you. ha im pretty sure the college board hates you by now..

[riceboi89]

I wish you were my calc professor

[TheLifeBeauty]

Wow... very clear..very easy to understand..

Thank u very much!!

[rararaRACHEL]

right now, you are my favorite person in the ENTIRE WORLD.

[hackersvirus90]

THX a lot :D:D i hope i pass my exams

[arias1772]

i have my calc 3 midterm in 2.5 hours and this helped alot lol

[igormon]

This is calc 2 stuff.

[arias1772]

@igormon im on quarter system.

[arias1772]

@igormon quarter system



[StarlightDragon]

You are a great teacher, you make my college calculus classes so much easier. I wish you taught at our university, lol. Thanks again! :D

[cc69cc]

gracias aweonao =)

[iMm3nUrD3D]

your videos are saving me life THANKYOU

[oexnorth]

What would you do for 1/(4+2^(-n))?

[FUCKYOURMOMINTHEASS2]

use the ratio test, it works out.

[Frankreif]

@oexnorth remember 2^2 = 4 . This allows simplification down to:

lim[ 2^(2-n) / 2^(2-n-1)]

[frenchpandas]

i appreciate your helpful videos, you are seriously the coolest

[tsd5060]

hOW IS IT #^3, AND NOT 3^-3?

[masterchief2744]

it would be 3^-3 if it were on top, 3^3 is on the bottom

[Avi0107]

thankssssssssssss

[yumibear05]

Fank you soooo much for all your help on these topics they do really help...better than my own lecture and text book we are to use!!!!

[cbearau09]

98 on my Cal 2 exam on Series and Sequences. Your videos were a big part of that!

[prettymuuch]

thanks so much i hope you realize how much help you've been!

[blackanesian]

idk why i watch these videos because im even taking this math

[vecr0]

"which really doesn't matter too much " :DD

[vizzo555]

Thanks you so much! Im doin Mech eng and your better than all my maths lecturers!

[Poke4Poker]

i totally got a 5 on my bc test. woot.

[patrickJMT]

that is great! good job!!

[YouGoddard]

In the example were you end up with n^2/n^3, isn't that the same as 1/n, which diverges by harmonic series?

[wrathof89]

For the Ratio Test we're taking a limit, so we didn't have a series of n^2/n^3, but a limit of that ratio...that limit is zero.

[NetDialect]

kewl thanks.

[Poke4Poker]

no he didn't end up with n^2/n^3 he ended up with something similar to that he just didnt feel like foiling..

[k2ngofchaos]

he could have just canceled the x+1 too, but i think the point was teaching the short cut

[Jezmeya]

u are a REALLY good teacher thanks alot :D

[L0stR3naissanc3]

thanks bro

[abettername]

Patrick. Thank you so much.

[lwdancer]

Thank you so much!! This is so helpful! I really appreciate it! :)

[moemyself3]

I really like the way you write sigma, i think i'll try it out for a while, see if i like it so i can adopt it. lol

[elghs2001]

I've already adopted it myself. I love it!  lol

[itsjustemilyy]

you are my hero :)

[SevereTstormFan]

Man oh man you are a lifesaver. You are working out all the small trouble spots I have and now I completely understand it. Thank you so much.

[kikanqa]

WOW u are awesome...I LOVE U!!!...u make math look easy...which gives me hope..thanks again :)

[nmq3b]

Hey Patrick! I just wanted to say that I was completely clueless on the factorial examples that my professor used to give, but when you said "think of it as 7! over 8!" etc, everything just cleared up.

Thank you so much man. I can't tell you how much I appreciate it.

[patrickJMT]

whenever you get stuck on the 'generic notation' try to use some concrete examples!!! that usually helps to clarify things!

glad the vid helped

[shivamappadu]

Thanks a lot for helping

[gandalfpres]

Sorry if this is a dumb question, but why does ((n+1)/n)^n go to e?

[gandalfpres]

Just answered my own question. I just learned e as (1+(1/n))^n. Same thing.

[vidhi18d]

thanx sir ur vedios help me lot ur gr8

[hoki121]

I haven't been to class in a few weeks because my professor is very hard to understand. I've been watching your videos instead...and i gotta say you are amazing. I wish you were my professor :) Thanks so much for posting these videos. Take care ^__^

[patrickJMT]

no problem : )

and.... go to class : )

[MarcMeWord]

You are my hero

[JulioUPC]

you help me a lot thank you soo much!!

[patrickJMT]

you are very welcome!

[comfycouch22]

will you ever make videos on diff equations, calc III or linear algebra?

[patrickJMT]

yes, and i already have a few

[ViadoMundo]

Thanks for video! Great as usual!

[titleysfury]

thanks mate, this really helps alot.

[catfish4975]

I'm so glad I found your lessons on here. I've been struggling with Calc II because my book is impossible to understand and my Professor goes too fast. I think this is going to save me. I found this two days ago and my understanding has increased tremendously and I don't feel intimidated by this stuff. Thank you. Please continue posting things!!!

[patrickJMT]

glad it helps! i will keep posting!

[allets90]

Thanks so much for all these helpful videos!

[patrickJMT]

no problem!

[redman332]

I *really* wish I would have found these videos last semester (I would have felt confident enough to take Calculus II in the summer rather than this semester).  But I am glad I found them when I did, and you can believe that I will be spreading word about these videos. Great job.

[patrickJMT]

thanks friend : )

glad you like them!

[brco2003]

You could've also canceled out the n+1's to make things a bit clearer in the end, but great vid

[chnsdragon]

Thank you soo much for all your video posts on Calculus. I hope you put more of these up. My professor isn't as clear and concise as yourself...so I have a hard time with most of the work presented. When you explain the material, I understand everything the first time! Once again thank you, your assistance is greatly appreciated!

[patrickJMT]

hey, glad to help! i appreciate the kind comments; it is nice to know that my hours and hours and hours of making and posting math vids is helping make things a bit clearer for others out there!! take care, and good luck.

[matador0731]

very clear professor.

[khnz786]

Thanks so much for posting this - you're very knowledgeable!

[sk070527]

hey keep the vids comin...ur explanations are better than the stupid textbook. the series vids really helped me out

[jonwalker80]

not sure why people are not giving a better rating...! this vid is very good (like all the rest!) thanks for posting these for us. : )