Math2400
  • Math2400
radius of convergence and the interval of convergence for the given power series
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Math2400
  • Math2400
\[\sum_{n=1}^{\infty} \frac{ n ^{2}x ^{2n} }{ n! }\]
Math2400
  • Math2400
my radius is 1. And it think the interval is (-1,1) Can anyone verify if that's right?
Zarkon
  • Zarkon
what test did you use?

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Math2400
  • Math2400
ratio
Zarkon
  • Zarkon
do it again
Math2400
  • Math2400
ok
Math2400
  • Math2400
wait can the radius be infinity??
Zarkon
  • Zarkon
yes
Math2400
  • Math2400
ok..and the interval is (-infin, infin) ?
Zarkon
  • Zarkon
yes
Math2400
  • Math2400
lol kk thanks. that's what i got first but i wasn't sure if that was possible haha
xapproachesinfinity
  • xapproachesinfinity
i got oo as well :)
Math2400
  • Math2400
perfect thanks!! :)
xapproachesinfinity
  • xapproachesinfinity
limit (x^2 . (n+1/n)^2/(n+1))=0
Math2400
  • Math2400
how 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
  • xapproachesinfinity
that says for any value of x rho is always zero
Math2400
  • Math2400
and then interval is (2,4) or maybe (2,4] not sure, i suck at these
xapproachesinfinity
  • xapproachesinfinity
i would do root test with that one
xapproachesinfinity
  • xapproachesinfinity
did you try ratio?
Zarkon
  • Zarkon
there is no x in your last problem
Math2400
  • Math2400
yes(: I got the radius to be 1 and then i know the interval is (2,4) but I'm not sure
xapproachesinfinity
  • xapproachesinfinity
eh hold on you are asking for convergence because there is not x
xapproachesinfinity
  • xapproachesinfinity
you need x
Math2400
  • Math2400
ohh wait sorry i posted the wrong one. That one is a converging series haha. I meant to post this one: \[\sum_{n=1}^{\infty} \frac{ (x-3)^n }{ \sqrt{n} }\]
xapproachesinfinity
  • xapproachesinfinity
oh ok i would go with root test with that too limit n^1/n=1 rho=|x-3|<1 so raduis is 1 -1 2
xapproachesinfinity
  • xapproachesinfinity
i guess you got this :)
Math2400
  • Math2400
ok so radius is 1 and then did u check the end points?
xapproachesinfinity
  • xapproachesinfinity
No 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
  • Math2400
so would it be (2,4] or just (2,4) that's what I'm confused on
xapproachesinfinity
  • xapproachesinfinity
no converge on 2 not on 4 so [2,4) otherwise 2<=x<4
Math2400
  • Math2400
ohh haha kk got it :) Thank you so much!
xapproachesinfinity
  • xapproachesinfinity
no problem :)
xapproachesinfinity
  • xapproachesinfinity
actually you seem to me good at this, just few more practice and you master it
Math2400
  • Math2400
haha thank you, means a lot @xapproachesinfinity

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