# How does sigma notation work?

Oct 14, 2014

Sigma notation can be a bit daunting, but it's actually rather straightforward. The common way to write sigma notation is as follows:

${\sum}_{x}^{n} f \left(x\right)$

Breaking it down into its parts:

• The $\sum$ sign just means "the sum".
• The $x$ at the bottom is our starting value for x. It usually has a number next to it: ${\sum}_{x = 0}$, for example, means we start at x=0 and carry on upwards until we hit...
• The $n$ at the top.
• The $f \left(x\right)$ is what we need to plug all these values into. At the end, we add the results obtained from here together, and that's our answer.

Note that it's not always $f \left(x\right)$ - it is most often $f \left(n\right)$ or $f \left(i\right)$.

As an example:

${\sum}_{x = 0}^{9} {\left(\sqrt{x} + 1\right)}^{2}$

means we need to find

${\left(\sqrt{0} + 1\right)}^{2} + {\left(\sqrt{1} + 1\right)}^{2} + {\left(\sqrt{2} + 1\right)}^{2} + \ldots + {\left(\sqrt{9} + 1\right)}^{2}$.