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October 24th, 2017, 08:18 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0  To what value does the infinite sum converge?
Observe the following infinite sum: Where d, v, and y are constants. To what value does it converge? 
October 25th, 2017, 04:26 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
I assume that y is an integer constant, otherwise, (n y)! makes no sense. But what about values of y larger than n? How are we to interpret (n y)! when n y is negative?

October 25th, 2017, 07:59 AM  #3  
Senior Member Joined: Sep 2015 From: USA Posts: 2,408 Thanks: 1310  Quote:
and $n,y \in \mathbb{N}+\{0\}$ and finally $y \leq n$ then $\displaystyle \sum_{n=y}^\infty \dfrac{d^n (1v)^{ny}}{(ny)!} = e^{d (1v)} d^y$ Last edited by romsek; October 25th, 2017 at 08:17 AM.  

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