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November 15th, 2016, 06:04 PM   #1
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Question Interval of Convergence

Im trying to find the interval of convergence of a series. I used the Ratio test for absolute convergence, but that limit ended up being zero. For the other problems i've done, it usually comes out to 1 and then i multiply that by |X| and find the I.O.C. Im not sure what that means when the limit is zero though.
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November 15th, 2016, 06:38 PM   #2
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maybe this is an example ...

$\displaystyle \sum_{n=0}^\infty \dfrac{x^n}{n!}$

$\displaystyle \lim_{n \to \infty} \bigg|\dfrac{x^{n+1}}{(n+1)!} \cdot \dfrac{n!}{x^n} \bigg|$

$\displaystyle |x| \cdot \lim_{n \to \infty} \dfrac{1}{n+1} = 0$

Interval of convergence is $-\infty <x< \infty$
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November 15th, 2016, 07:09 PM   #3
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Ok thanks, but why is it -infinity to infinity, i dont really get it.
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November 15th, 2016, 07:35 PM   #4
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$|x| \cdot 0 < 1$ ... for what values of x is that inequality true?

Last edited by skeeter; November 15th, 2016 at 07:38 PM.
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November 15th, 2016, 07:37 PM   #5
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Okay that makes sense now, thanks a lot.
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