Sum of series $\frac{n}{(n+1)!}$ I'm encountering some difficulty on a question for finding the sum of the series $$\sum_{n=0}^\infty \dfrac{n}{(n+1)!}$$
The method I use to tackle this type of problem is generally to find a similar sum of a power series and algebraically manipulate it to match that of the original. I haven't found anything similar except for the summation of $e^x$ starting from $n=-1$, and subbing in $n^{\frac{1}{n}}$. Though, I'm not sure that will even work.
Thanks in advance for any help/advice!

hint:
$$ \sum_{n=0}^\infty \dfrac{n}{(n+1)!}=   \sum_{n=1}^\infty \dfrac{n-1}{(n)!}$$
