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Does the following series converge or diverge?

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

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    Some of the answers to your [previous question](http://math.stackexchange.com/questions/163882/does-the-sequence-fracn2n-converge-or-diverge) from a few hours ago could be adapted to help here. For example, [Cameron Buie's answer](http://math.stackexchange.com/a/163908/1424) showed how you can see that $\sum \dfrac{2^n}{n!}$ converges, and the method can be adapted here, (e.g. using n<4^n or the way Marvis did it). It would be appreciated by some (many, I think) if you indicate what you tried before asking.2012-06-28

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$\sum_{n=1}^{\infty} \dfrac{4^n + n}{n!} = \sum_{n=1}^{\infty} \dfrac{4^n}{n!} + \sum_{n=1}^{\infty} \dfrac{n}{n!} = \exp(4)-1 + \sum_{n=1}^{\infty} \dfrac1{(n-1)!} = \exp(4)-1 + \exp(1)$

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    I miss the easiest part. I didn't think about splitting it into two series! Thank you very much!2012-06-27