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Math Help - finding the sum of a series

  1. #1
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    finding the sum of a series

    Find the sum of the series \sum \frac{3k}{(k+1)!} from k=1 to infinity.
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  2. #2
    Eater of Worlds
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    Compare to the series for e at x=1 and maybe you can see something.

    \frac{k}{(k+1)!}=\frac{1}{k!}-\frac{1}{k!(k+1)}
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  3. #3
    MHF Contributor chisigma's Avatar
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    The constant 3 can be 'pulled out' from the summation so that is...

    3\cdot \sum_{k=1}^{\infty} \frac {k}{(k+1)!} = 3\cdot \sum_{n=2}^{\infty} \frac{n-1}{n!}= 3\cdot \{\sum_{n=1}^{\infty} \frac{1}{n!} - \sum_{n=2}^{\infty} \frac{1}{n!}\} = 3

    Kind regards

    \chi \sigma
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