
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 24th, 2017, 09:18 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, 05:26 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 
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, 08:59 AM  #3  
Senior Member Joined: Sep 2015 From: USA Posts: 2,304 Thanks: 1221  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 09:17 AM.  

Tags 
converge, infinite, sum 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Does it converge?  edwinpaco  Real Analysis  2  May 8th, 2017 08:25 AM 
Infinite intersections and infinite unions  Azzajazz  Real Analysis  5  March 10th, 2016 09:01 PM 
Relation between an infinite product and an infinite sum.  Agno  Number Theory  0  March 8th, 2014 05:25 AM 
Infinite series that only converge for Re(s)=1/2.  Agno  Number Theory  1  December 30th, 2013 10:05 AM 
Infinite set contains an infinite number of subsets  durky  Abstract Algebra  1  March 15th, 2012 12:28 PM 