# Summation

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

$$\sum_{i=1}^{n} f(i) = f(1) + f(2) + ... + f(n)$$

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.

$$\sum_{i=1}^{n} c = nc$$ $$\sum_{i=1}^{n} 1 = n$$ $$\sum_{i=1}^{n} i = \frac{n(n + 1)}{2}$$ $$\sum_{i=1}^{3} i^2 = 1^2 + 2^2 + 3^2 = 14$$

## Product

A similar notation is used to convey iterative multiplication.

$$\prod_{i=a}^{b} f(i)$$