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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. Tags converge, infinite, sum Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post edwinpaco Real Analysis 2 May 8th, 2017 07:25 AM Azzajazz Real Analysis 5 March 10th, 2016 08:01 PM Agno Number Theory 0 March 8th, 2014 04:25 AM Agno Number Theory 1 December 30th, 2013 09:05 AM durky Abstract Algebra 1 March 15th, 2012 11:28 AM

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