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.


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}


A similar notation is used to convey iterative multiplication.

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