sum of sequence

## Primary tabs

# sum of sequence

Submitted by anirban_mandal on Fri, 01/29/2010 - 18:48

Forums:

what is the sum of the following sequence as a function of 'n'.

1*1! + 2*2! + 3*3! + ...... + n*n!

would be a great help if someone could say how i should approach the problem.

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections

## Versions

(v1) by anirban_mandal 2010-01-29

## Re: sum of sequence

Sum(1,n)k*k!= Sum(1,n)(k+1)k! - Sum(1,n)k!

Sum(1,n)(k+1)k!= Sum(2,n+1)k!

Combine to get (n+1)! - 1

## Re: sum of sequence

[;(2-1)\cdot 1! +(3-1)\cdot 2! + \dots + (n+1 -1)\cdot n!=\left( \sum_{i=2}^{n+1}i! \right) - \left( \sum_{i=1}^{n}i! \right)=(n+1)!-1;]