Sunday, 8 December 2013

calculus - Determining the sum of a series as a function of the variable x

I have the following series:
$$
\sum_{n=0}^\infty (-1)^n \frac{x^{9n}}{n!}
$$

I want to find the sum of the series of as a function of $x$.



It seems to resemble the Taylor series where of $e^x$ which is $\sum_{n=0}^{\infty} \frac{x^n}{n!}$.




I have also considered it as a telescoping series (which is not) and a geometric series ( which also does not seem to be the case).



How should I approach this problem ?



questionathand

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