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Math Help - Quickie #6

  1. #1
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    Quickie #6

    Find the sum of the series:

    . . 1(1!) + 2(2!) + 3(3!) + \cdots + n(n!)
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  2. #2
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    Quote Originally Posted by Soroban View Post
    Find the sum of the series:

    . . 1(1!) + 2(2!) + 3(3!) + \cdots + n(n!)
    Quick already solved it.
    (n+1)!-1

    It is just mathematical iduction
    Last edited by ThePerfectHacker; December 30th 2006 at 02:35 PM.
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  3. #3
    TD!
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    I don't know where it was solved, but even without (explicit) induction:

    <br />
k\left( {k!} \right) = \left( {k + 1} \right)k! - k! = \left( {k + 1} \right)! - k!<br />

    So summing for k = 1 till n gives (n+1)!-1 since all intermediate terms cancel out.
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