# Summation

A summation is a concise expression describing the addition of an arbitrarily large set of numbers. A capital sigma is denotes summation.

\begin{equation} \sum_{i=1}^{n} f(i) = f(1) + f(2) + ... + f(n) \end{equation}
Here, \(m\) is the **lower bound** and \(n\) is the
**upper bound**. The summation starts at \(m\) and ends at \(n\).
\(i\) is the **index of summation**.

## Examples

Simple closed forms exist for many algebraic functions.

\begin{equation} \sum_{i=1}^{n} c = nc \end{equation} \begin{equation} \sum_{i=1}^{n} 1 = n \end{equation} \begin{equation} \sum_{i=1}^{n} i = \frac{n(n + 1)}{2} \end{equation} \begin{equation} \sum_{i=1}^{3} i^2 = 1^2 + 2^2 + 3^2 = 14 \end{equation}## Product

A similar notation is used to convey iterative multiplication.

\begin{equation} \prod_{i=a}^{b} f(i) \end{equation}