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Math Help - sums

  1. #1
    Senior Member
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    sums

    Find the sum of

     <br />
\sum^n_{r=1}r(r!)<br />
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  2. #2
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    Try proving by induction, that:

    \sum^n_{r=1}r(r!) = (n+1)! - 1
    Last edited by Defunkt; September 12th 2009 at 12:04 PM.
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  3. #3
    MHF Contributor red_dog's Avatar
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    \sum_{r=1}^nr\cdot r!=\sum_{r=1}^n(r+1-1)r!=\sum_{r=1}^n[(r+1)!-r!]=\sum_{r=1}^n(r+1)!-\sum_{r=1}^nr!=

    =2!+3!+\ldots+n!+(n+1)!-1!-2!-3!-\ldots-n!=(n+1)!-1
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