一些生成函数

\[1 + x^2 + x^3 + ... = \frac{1}{1 - x} \]

\[1 + (kx)^2 + (kx)^3 + ... = \frac{1}{1 - kx} \]

\[1 + x^2 + x^3 + ... + x^n = \frac{1 - x^{n + 1}}{1 - x} \]

\[\sum_{i = 0} ^\infty {C_{i + k - 1}^{k - 1}x^i} = \frac{1}{(1 - x)^k} \]