Prove:
for and .
I considered but got stuck at manipulating double sums. Please help
FIRST, it must be pointed out that the is a mistake in the question.
This is Vandermonde's Theorem it should be
We can do a combinational proof.
is the number of ways to choose k items from m+n.
If then is the number of ways to choose those k items with j coming from the m group and k-j coming from the n group.
Now it us easy to see that
.