# Coefficient of x in a geometric sum raised to the power of n

I have an exam in 6 hours I can't work out how to do these questions. Any help would be greatly appreciated.

a) Compute the coefficient of the term $$x^{70}$$ in the expansion of the polynomial $$(1 + x + x^2 + \dots + x^{70})^6$$.

b) Compute the coefficient of the term $$x^{70}$$ in the expansion of the polynomial $$(1 + x + x^2 + \dots + x^{20})^6$$.

Note that $$(1+x+\dots+x^{n-1})^m = (1- x^n)^m(1 - x)^{-m}.$$
Then one may use binomial theorem: $$(1- x^n)^m = \sum_{k=0}^{m}(-1)^k\binom{m}{k}x^{nk},$$ $$(1- x)^{-m} = \sum_{k=0}^{\infty}(-1)^k\binom{-m}{k}x^{k} = \sum_{k=0}^{\infty}\binom{m+k-1}{k}x^{k}.$$ Now it's easy to compute coefficient $C_q$ of the term $x^q$ in the whole expansion: $$C_q = \sum_{nk_1+k_2=q}(-1)^{k_1}\binom{m}{k_1}\binom{m+k_2-1}{k_2}.$$