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Math Help - Need help with the exact sum of convergent series

  1. #1
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    Need help with the exact sum of convergent series

    Please help with the following:

    Find the exact sum of the following convergent series:

    sum from n=0 to infinity of (2n/(3nn!))

    Thanks!
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  2. #2
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    Re: Need help with the exact sum of convergent series

    You should know that \displaystyle \begin{align*} e^x = \sum_{n = 0}^{\infty} \frac{x^n}{n!} \end{align*}.

    Notice that \displaystyle \begin{align*} \frac{2^n}{3^n \, n!} = \frac{2^n}{3^n} \cdot \frac{1}{n!} = \left( \frac{2}{3} \right)^n \cdot \frac{1}{n!} = \frac{\left( \frac{2}{3} \right)^n }{n!} \end{align*}.

    What do you think your sum has to equal?
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  3. #3
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    Re: Need help with the exact sum of convergent series

    Is it e^(2/3)?
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    Re: Need help with the exact sum of convergent series

    Quote Originally Posted by kimsanders82 View Post
    Is it e^(2/3)?
    Yes, well done
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