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} ]