How does sigma notation work?

1 Answer
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)^nf(x)nxf(x)

Breaking it down into its parts:

  • The sum sign just means "the sum".
  • The xx at the bottom is our starting value for x. It usually has a number next to it: sum_(x=0)x=0, for example, means we start at x=0 and carry on upwards until we hit...
  • The nn at the top.
  • The f(x)f(x) 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(x)f(x) - it is most often f(n)f(n) or f(i)f(i).

As an example:

sum_(x=0)^9(sqrt(x)+1)^29x=0(x+1)2

means we need to find

(sqrt(0)+1)^2+(sqrt(1)+1)^2+(sqrt(2)+1)^2+...+(sqrt(9)+1)^2.