# Summation of a Product of Functions

1. May 19, 2012

### drewfstr314

Is there a general formula for something like

$\sum_{n=0}^{\infty} \left( f(n) \times g(n) \right)$

For example, what is

$\sum_{n=0}^{\infty} \left( 3^n \times \frac{n!}{n^2} \right)$

2. May 19, 2012

### micromass

Infinity, since the series diverges.

3. May 20, 2012