# Summation question

1. May 15, 2010

### donutmax

$$\sum_{n=0}^{\infty} \frac{2^{n+1}(n+1)t^n}{(n+2)!}=\sum_{n=0}^{\infty} \frac{2^{n}nt^{n-1}}{(n+1)!}$$

How are the above summation equal?

2. May 15, 2010

### Landau

Since $\sum_{n=0}^\infty a_n=a_{0}+\sum_{n=0}^\infty a_{n+1}$, and $a_0$ happens to be zero.