Prove:

for and .

I considered but got stuck at manipulating double sums. Please help (Crying)

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- Nov 8th 2011, 05:35 AMCuriosityCabinetProof of binomial sums
Prove:

for and .

I considered but got stuck at manipulating double sums. Please help (Crying) - Nov 8th 2011, 05:49 AMseldRe: Proof of binomial sums
Have you looked at this property?

So for example:

This may help a little. - Nov 8th 2011, 05:54 AMveileenRe: Proof of binomial sums

The second sum is the coefficient of from .

- Nov 8th 2011, 08:01 AMPlatoRe: Proof of binomial sums
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 chooseitems from*k*.*m+n*

If then is the number of ways to choose thoseitems with*k*coming from the*j*group and*m*coming from the*k-j*group.*n*

Now it us easy to see that

.