Solving the Series: sum_{r=0}^{+\infty}1/(r*r!)

mathsnerd · Sep 10, 2008

I'm trying to find the sum of the following series and am a bit stuck:

sum_{r=0}^{+\infty}1/(r*r!)

It looks a bit like e^1 but the extra r in the denominator is causing problems. Can anyone help?

dirk_mec1 · Sep 10, 2008

Where does this problem originates from?

mathsnerd · Sep 11, 2008

It's part of a birth rate for a birth and death process in a particular special case. The series looks like it should be summable but I can't think how to do it.

Solving the Series: sum_{r=0}^{+\infty}1/(r*r!)

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