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October 11th, 2017, 09:15 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0  Simplify the sum
How would you simplify the following sum? The parentheses refer to combinations (n choose r). The outcome should be a function of y. However, I cannot figure out how to simplify this. Any recommendations? 
October 11th, 2017, 10:20 PM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,165 Thanks: 1139 
Mathematica chugged away at it for a while and didn't come up with anything.

October 12th, 2017, 04:36 PM  #3 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 
I figured it out. It's Vandermonde's identity. https://en.wikipedia.org/wiki/Vandermonde%27s_identity 

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