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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
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Quote:
 Originally Posted by John Travolski Observe the following infinite sum: Where d, v, and y are constants. To what value does it converge?
If you assume $d,v \in \mathbb{R}$

and

$n,y \in \mathbb{N}+\{0\}$

and finally

$y \leq n$

then

$\displaystyle \sum_{n=y}^\infty \dfrac{d^n (1-v)^{n-y}}{(n-y)!} = e^{d (1-v)} d^y$

Last edited by romsek; October 25th, 2017 at 08:17 AM.

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