Series Expansions
In mathematics, given an infinite sequence of numbers {an}, a series is informally the result of adding all those terms together. These can be written more compactly using the summation symbol ∑. An example is the famous series from Zeno's Dichotomy:

 
\sum_{n=1}^\infty \frac{1}{2^n} = \frac{1}{2}+ \frac{1}{4}+ \frac{1}{8}+\cdots+ \frac{1}{2^n}+\cdots from Wikipedia - RF Cafe

The terms of the series are often produced according to a certain rule, such as by a formula, by an algorithm, by a sequence of measurements, or even by a random number generator. As there are an infinite number of terms, this notion is often called an infinite series. Unlike finite summations, series need tools from mathematical analysis to be fully understood and manipulated. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics and computer science. - Wikipedia

Taylor's Series
RF Cafe: Taylor's Series
Binomial Expansion
RF Cafe: Binomial Expansion
Exponential Expansion Logarithmic Expansion
RF Cafe: Exponential Expansion RF Cafe: Logarithmic Expansion
Sine Expansion Cosine Expansion
RF Cafe: Sine Expansion RF Cafe: Cosine Expansion
θ expressed in radians