Sum of $\sum_{n=1}^{+\infty}\frac{1}{(n-1)! +n!}$ I have to compute the nature of this series, and if it converges, the sum of it. I just can't find the proper way to get to the partial form, from where I can simplify the parts. I've tried writing $(n+1)!+n!$ as $(n-1)!(1+n)$, but that didn't work either.
$$\sum_{n=1}^{+\infty}\frac{1}{(n-1)!+n!}$$

Almost there. Observe that
$$\frac 1{(n-1)!+n!} = \frac 1{(n-1)!(n+1)} = \frac n{(n+1)!} = \frac {n+1}{(n+1)!} - \frac 1{(n+1)!} = \frac1{n!} - \frac1{(n+1)!}$$
Do you see how it telescopes?
