Monotonic Ordinary Generating Functions

SECTIONS

Geometric Series

\displaystyle \dfrac{a}{1-x} = \sum_{n \geq 0} a \, x^n = a + ax + ax^2 + ax^3 + ax^4 + ax^5 + \cdots \

\displaystyle \dfrac{1}{1-ax} = \sum_{n \geq 0} a^n \, x^n = 1 + ax + (ax)^2 + (ax)^3 + (ax)^4 + (ax)^5 + \cdots \

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