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Pardon me if this is a stupid question, but this is my first time doing Power Series. The question is:

Find the radius of convergence and interval of convergence for the series.

$$ \sum_{n=0}^{\infty} \frac{x^{n+1}}{4n!} $$

Here what I tried: Work

This gives me a radius of convergence of 0, which certainly cannot be right. Can someone help point me in the right direction?

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    $\begingroup$ No, the outcome of the Ratio test is zero. This means that the interval of convergence is the real number line (the series converges for any chosen $x$) so we are talking about a very BIG radius..... $\endgroup$ – imranfat Mar 27 '17 at 18:23

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