Given that
is a polynomial of degree r in M, find r and the coefficient of .(The coefficient is an integer)
Any ideas how to go about solving this problem?
I have no idea how to prove it, but this formula is what you are looking for. It says . Put n=2M+1 and you get .
Notice that the sum goes from 1 to 2M. But using the fact that you can see that this is twice the sum from 1 to M.