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?

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- Oct 13th 2008, 11:06 AMHweengeeHelp with summation
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? - Oct 13th 2008, 11:37 PMMoo
- Oct 14th 2008, 04:16 AMHweengee
I have no idea. I am allowed to use MAPLE, but the command sum(expression,m=1..M) doesn't give a general solution in a polynomial form, so I am quite confused. And we haven't gotten to sequences and series in my calculus course yet.

- Oct 14th 2008, 10:19 AMOpalg
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.