Theorem T79 ∑j=0njxj=nxn+2−(n+1)xn+1+x(x−1)2\sum_{j=0}^n j x^j = \frac{n x^{n + 2} - (n + 1) x^{n + 1} + x}{(x - 1)^2} j=0∑njxj=(x−1)2nxn+2−(n+1)xn+1+x for x≠1x \neq 1x=1.