If , show that

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- Jan 22nd 2009, 02:48 AMalexmahoneBinomial theorem
If , show that

- Jan 22nd 2009, 03:52 AMPaulRS
That is equivalent to showing that: (1)

To prove it:

Now consider the coefficient of in the product:

It is: this last equality holds since:

NOw, on the other hand:

So from here we also want the coefficient of , which is exactly the RHS of (1) -by using the binomial theorem-, now, from the uniqueness of the coefficients of the polynomials it follows that - Jan 22nd 2009, 05:50 AMpankaj
- Jan 22nd 2009, 06:01 AMalexmahone
- Jan 22nd 2009, 07:06 AMpankaj

This is number of ways to select n objects from 2n objects which is alternatively