Help Factorial Partial Fraction Decomposition

[danerape]

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]

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]

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

 

[danerape]

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

 

[dextercioby]

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

 

[danerape]

Wow, that is pretty obvious, I haven't had any experience with ! before this though. Thanks a lot!

Dane