# Homework Help: Infinite limit of factorial series

1. Jul 5, 2011

### flyerpower

1. The problem statement, all variables and given/known data

3. The attempt at a solution

I have no idea where to start from.
I know that e = 1/0! + 1/1! + 1/2! + 1/3! + .......... + 1/n! + .....
and tried to separate the factorial off the geometric series but had no success.

2. Jul 5, 2011

### tarantella

We start from $$\frac{2^{k-1}(k-1)}{(k+1)!} =\frac{2^{k-1}(k+1-2)}{(k+1)!} = \frac{2^{k-1}}{k!}-\frac{2^k}{(k+1)!}$$ and we recognize a telescopic series.