# Homework Help: Help! Factorial Partial Fraction Decomposition

1. Nov 21, 2011

### danerape

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

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

2. Nov 21, 2011

### vela

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

3. Nov 21, 2011

### dextercioby

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

4. Nov 21, 2011

### danerape

Wow, sorry. I meant n/(n+1)!=1/n! - 1/(n+1)!

5. Nov 21, 2011

### dextercioby

It's easy to prove. In the LHS write n=(n+1)-1.

6. Nov 21, 2011

### danerape

Wow, that is pretty obvious, I haven't had any experiance with ! before this though. Thanks alot!!!!

Dane