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 August 11th, 2013, 02:29 PM #1 Newbie   Joined: Aug 2013 Posts: 4 Thanks: 0 Evaluating a series with factorial Here is the question: Evaluate sigma notation (from k=0 to infinity) (1/((e^k)(k!))) Thank you very much!
 August 11th, 2013, 03:21 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Evaluating a series with factorial Using the Maclaurin series: $e^{x}= \sum^{\infty}_{n=0} \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots\quad\text{ for all } x\!$ We then see that: $\sum_{k=0}^{\infty}\frac{1}{e^kk!}=\sum_{k=0}^{\in fty}\frac{$$\frac{1}{e}$$^k}{k!}=e^{\frac{1}{e}}$

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