# Sum this series

1. Nov 22, 2012

### utkarshakash

1. The problem statement, all variables and given/known data
1.1!+2.2!+3.3!.......n terms

2. Relevant equations

3. The attempt at a solution
The first part of every term is in AP whose cd is 1. Also the nth term of this series is given as n.n! If I expand it it becomes n.n(n-1)(n-2).......1

Now
$S_n=\sum t_n \\ = \sum n.n(n-1)(n-2)......1$

But now how do I compute this summation?

2. Nov 22, 2012

### Mentallic

Consider n = (n+1)-1

3. Nov 22, 2012

### utkarshakash

I didn't get you. What you said was to replace all the n's with (n+1)-1 but I didn't find it to be helpful. Can you please give me some more hints?

4. Nov 22, 2012

### Mentallic

Not all n's!

n.n! = [(n+1)-1]n!