Generating function for a sequence
The question is as follows:
It is known that the generating function for the sequence , {1,8,27,64,...} is
[x(x^2 + 4x +1)]/(1-x)^4
Use the result to show summation from r=1 to n of r^3 = [n^2(n^2+1)]/4
I know i have to find the sequence represented by 1,8,27,64, .. and once i get the sequence i have to manipulate it until i reach r^3 which will be given by the expression.
My problem is that i cannot find the sequence for 1,8,27,64,...
any help please???
Thank buches!