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sum of sequence

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sum of sequence

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.


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

[;(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;]

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