Question

How does sigma notation work?

Answer 1

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)`

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(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)` - it is most often `f(n)` or `f(i)`.

As an example:

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

means we need to find

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