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Math Help - sum to infinity

  1. #1
    Junior Member
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    sum to infinity

    how do i find the sum to infinity of the sum of (2r+1)/r! where r>=1. i have no clue about sums and factorials.
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  2. #2
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    Re: sum to infinity

    \sum_{r = 1}^{\infty} \frac{1}{r!} = e-1

    2 \sum_{r = 1}^{\infty} \frac{r}{r!} = 2 \sum_{r = 1}^{\infty} \frac{1}{(r-1)!} = \sum_{r = 0}^{\infty} \frac{1}{r!} = e (simply shifted the "index" by 1)

    Adding, we get

    \sum_{r = 1}^{\infty} \frac{2r+1}{r!} = 2e + (e-1) = 3e - 1
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