Does the following series converge or diverge?
$$\sum_{n=1}^\infty\frac{4^n+n}{n!}$$
2026-04-09 13:29:44.1775741384
Does the series converge or diverge? $\sum_{n=1}^\infty\frac{4^n+n}{n!}$
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$$\sum_{n=1}^{\infty} \dfrac{4^n + n}{n!} = \sum_{n=1}^{\infty} \dfrac{4^n}{n!} + \sum_{n=1}^{\infty} \dfrac{n}{n!} = \exp(4)-1 + \sum_{n=1}^{\infty} \dfrac1{(n-1)!} = \exp(4)-1 + \exp(1)$$