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I just ran into an expression, and I would like to know what it converges to. $\sum^{\infty}_{n=1} \frac{n}{(n-1)!}$

Do you know if it converges to something (like $e$) or, in alternative, how to find out what it converges to?

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    Thanks for fixing the equation.2012-06-25

1 Answers 1

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$\sum_{n=1}^{\infty} \dfrac{n}{(n-1)!} = \sum_{n=1}^{\infty} \dfrac{n-1+1}{(n-1)!} = \sum_{n=2}^{\infty} \dfrac1{(n-2)!} + \sum_{n=1}^{\infty} \dfrac1{(n-1)!} = e + e = 2e$

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    Any faster the answer would have come before the question!\2012-06-25