Ratio Test -- Radius of Convergence | MIT 18.01SC Single Variable Calculus, Fall 2010

[Calvin1087Elva]

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[Blackfate416]

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[melisantika]

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[anakmudajaman]

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[khoeruloemam]

your explanation is very vivid. I can understand. Thank you...Hopefully one day, I can study in MIT..

[JGalz]

Luckies. :p We have to test the end points and get the interval of convergence too. Lameeee. Thanks for the great video though .

[YUH186]

thanks !!

[sajeeds05]

thanks so much! I learnt so much and it was certainly informative :)..

[26877271]

Ma'am this video was a great help to me!

Thanks alot for posting MIT lectures :)

[Krotazazz]

The series in the last example is actually hyperbolic cosine, aka cosh(x), which is not alternating like cosine :-)

[Krotazazz]

dandaman113 is surely right, it is missing the (-1)^n factor. Other than that, an absolutely explicit and concise explanation of radius of convergence.

[dandaman113]

Good lecture. The last series though is not cosine -- cosine has an additional (-1)^n factor. It is an alternating series.

[pwnagenation1]

OMG THANK YOU, I was trying to determine what to do when lim n-->infinity of some n times x and it finally got explained at the end and i havent found it anywhere!

[emredodii]

Thanks for explaining that the limit of (x/n+1) is 0 because x is fixed and outrun by n+1. My textbook just skips directly to 1/n+1, which made me believe I couldn't do basic algebra.

[fp2k69]

Very helpful video. Thank you for streaming this. Really helped me!.... Lovely instructor too :D

[mwmnjs]

Great video!!!

[7ood]

Shakira math teacher

[Platemaster]

Her enthusiasm is admirable

[omzdog]

@Platemaster

alright gramps, go back to bed

[GuiLbAs]

you're an excelent teacher!

[jwexler2]

a real math teacher, wish binghamton had those

[MeSooCrazyy]

Nice video^^Btw how did you study to write so fast on the desk ?:P

[0921435280]

interesting teaching style

[deadlybug]

Sure was!

[dominicdill]

For the third example, why is the limit as n approaches infinity of n/(n+1) = 1? Wouldn't this be infinity over infinity which does not simplify to 1?

[Kj4235]

@dominicdill no it is 1, think it as 1000000000000000/1000000000000­001=0,9999999999999999

result becomes even more closer to 1 when you take bigger n values.

[bigbawsdogg]

@dominicdill take the limits dude: consider lim x--->infinity of x/(x+1) = lim----->infinity of 1/(1+1/x) = 1

[danesh007]

they don't?

[ssims619]

you would think MIT would have white boards...

[bigbawsdogg]

@ssims619 white boards are gay believe me the amount of times you cant see shit the lecturers writing. Plus white boards are more expensive.

[pjflameboy]

great video really helpful way of learning ratio test

[ZiaNM811]

Ex 4: helped me clear up a question about symplifing factorial problems. I do believe though that cosx = the sum (-1)^n(x^2n/2n!) from n=0 to infinety because it is a alternating series. However, adding (-1)^n does not change the outcome.

[thaiazngrl510]

wow you are so helpful! You are much clearer than my professor. Thank You :)

[onayr36]

This video really helped clear up the idea of radius of convergence for me thanks!

[Seshane1]

Very helpful. Thank you!

[userisdosser]

why my tutors are always men???