Find the sum to $n$ terms as well as the sum to infinity of the series:
$$\frac{1}{3} + \frac{1}{4\cdot 2!} + \frac{1}{5\cdot 3!} +\cdots.$$
I was trying this question many times but I didn't get the answer. I was using geometric series formula, but it was not applicable here...I don't know where I have to start, and I don't know any hint about this series....
If anybody helps me, I would be very thankful to him.
Each term is $$\frac1{(n+2)n!}.$$
Write this as $$\frac{n+1}{(n+2)!} =\frac{(n+2)-1}{(n+2)!} =\frac1{(n+1)!}-\frac1{(n+2)!} $$ and the sum telescopes.