Here is an interesting infinite series. It would be great to see a method to evaluate it, if possible. I know it converges to a little less than 11/40
$\displaystyle\sum_{k=1}^{\infty}\frac{1}{4^{k}+k!}$
I could not think of any good identities to start this.
Thanks a million to those who can show how to evaluate it.
Maybe even in general, $\displaystyle\sum_{k=1}^{\infty}\frac{1}{x^{k}+k!}$, where $x\geq 1$