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Math2400
 one year ago
radius of convergence and the interval of convergence for the given power series
Math2400
 one year ago
radius of convergence and the interval of convergence for the given power series

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Math2400
 one year ago
Best ResponseYou've already chosen the best response.1\[\sum_{n=1}^{\infty} \frac{ n ^{2}x ^{2n} }{ n! }\]

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1my radius is 1. And it think the interval is (1,1) Can anyone verify if that's right?

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1wait can the radius be infinity??

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1ok..and the interval is (infin, infin) ?

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1lol kk thanks. that's what i got first but i wasn't sure if that was possible haha

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1i got oo as well :)

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1limit (x^2 . (n+1/n)^2/(n+1))=0

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1how about this one if u don't mind: \[\sum_{n=1}^{\infty} \frac{ n^{e} }{ e ^{n} }\] i'm pretty sure the radius is 1 right?

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1that says for any value of x rho is always zero

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1and then interval is (2,4) or maybe (2,4] not sure, i suck at these

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1i would do root test with that one

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1did you try ratio?

Zarkon
 one year ago
Best ResponseYou've already chosen the best response.2there is no x in your last problem

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1yes(: I got the radius to be 1 and then i know the interval is (2,4) but I'm not sure

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1eh hold on you are asking for convergence because there is not x

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1you need x

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1ohh wait sorry i posted the wrong one. That one is a converging series haha. I meant to post this one: \[\sum_{n=1}^{\infty} \frac{ (x3)^n }{ \sqrt{n} }\]

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1oh ok i would go with root test with that too limit n^1/n=1 rho=x3<1 so raduis is 1 1<x3<1 ===> 2<x<4

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1i guess you got this :)

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1ok so radius is 1 and then did u check the end points?

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1No i didn't x=4 you have series 1/n^1/2 diverges x=2 (1)^n/rootn i believe this converge by alternating series test

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1so would it be (2,4] or just (2,4) that's what I'm confused on

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1no converge on 2 not on 4 so [2,4) otherwise 2<=x<4

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1ohh haha kk got it :) Thank you so much!

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1no problem :)

xapproachesinfinity
 one year ago
Best ResponseYou've already chosen the best response.1actually you seem to me good at this, just few more practice and you master it

Math2400
 one year ago
Best ResponseYou've already chosen the best response.1haha thank you, means a lot @xapproachesinfinity
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