# Find the sum to n terms as well as the sum to infinity of the series:

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.

• Hint: this looks like the integral of $x^2e^x$ at $x=1$...or something close to that. – lulu Aug 17 '17 at 13:10

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.