Find the generating function for compositions of n in which each part is at least 3, and the number of parts is at most 100.
So what I've tried is making the set of allowed parts P = {3,4,5,.....}, which leads to the generating function x^3/(1-x) . Then, I would have the sum from k=0 to 100 of (x^3/(1-x))^k which is my attempt of getting all lengths of the composition at most 100. I cant seem to go further then this and wanted tips on how to approach this and where my approach may be problematic. Thank you!
What you have done is correct. Now use the formula for a finite geometric series, with $r=x^3/(1-x)$.