# Help! Factorial Partial Fraction Decomposition

## Homework Statement

Show that n/(n+1)!=(1/n)-(1/(n+1)!)

I am totally lost on the algebraic steps taken to come to this conclusion. It is for an
Infinite series.

Thanks

vela
Staff Emeritus
Homework Helper
It's not true. For example, take n=3. Then
$$\frac{n}{(n+1)!} = \frac{3}{4!} = \frac{3}{24} = \frac{1}{8}$$but
$$\frac{1}{n}-\frac{1}{(n+1)!} = \frac{1}{3}-\frac{1}{24} = \frac{8}{24}-\frac{1}{24} = \frac{7}{24}$$

dextercioby