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Math Help - Decreasing series

  1. #1
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    Decreasing series

    How to prove that for a>0 and s_j = \sum_{i=0}^j \frac{a^i}{i!} the series
     f_j = \frac{s_j}{s_{j-1}}
    is decreasing?

    Thanks in advance!
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  2. #2
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    Re: Decreasing series

    Quote Originally Posted by sander View Post
    How to prove that for a>0 and s_j = \sum_{i=0}^j \frac{a^i}{i!} the series
     f_j = \frac{s_j}{s_{j-1}}
    is decreasing?

    Thanks in advance!
    Wouldn't \displaystyle \begin{align*} f_j \end{align*} be a sequence, not a series?
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  3. #3
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    Re: Decreasing series

    The series \sum_{i=0}^\infty\frac{a^i}{i!} converges to e^a.
    Last edited by HallsofIvy; July 21st 2012 at 07:40 AM.
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