Summation using generating functions

[mrRed]

How to calculate sum

\sum_{k=0}^{500} {3000 -2k \choose 2000}{2001 \choose k}

using method of generating functions?

 

[Ishuda]

How to calculate sum

\sum_{k=0}^{500} {3000 -2k \choose 2000}{2001 \choose k}

using method of generating functions?

First, you need to put a [t e x] [/t e x] tag pair around the LaTex in the forum [without the spaces in the 't e x' of course]. However, that doesn't seem to take care of the space issue, i.e. the expression becomes
\(\displaystyle \sum_{k=0}^{500} {3000 -2k \choose 2000}{2001 \choose k}\)


So, formatting the LaTex a bit differently, I think you have the question:

How to calculate the sum
\(\displaystyle \sum_{k=0}^{500}\,\, \left( {\begin{array} {*{20}c} 3000-2k \\2000\end{array}} \right)\, \left( {\begin{array}{*{20}c} 2001 \\k\end{array}} \right)\)
using the method of generating functions?