Math — Taylor & Maclaurin Series
Power-series expansions of common functions.
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f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x-a)^n
e^x = \sum_{n=0}^{\infty}\frac{x^n}{n!}
\sin x = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!}
\frac{1}{1-x} = \sum_{n=0}^{\infty} x^n \quad (|x|<1)