Solving Summations of n.n! Terms

[utkarshakash]

Homework Statement

1.1!+2.2!+3.3!...n terms

Homework Equations

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 \\<br /> = \sum n.n(n-1)(n-2)...1

But now how do I compute this summation?

 

[Mentallic]

Consider n = (n+1)-1

 

[utkarshakash]

Consider n = (n+1)-1

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?

 

[Mentallic]

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?

Not all n's!

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