# Calculus/Summation notation

Summation notation allows an expression that contains a sum to be expressed in a simple, compact manner. The uppercase Greek letter sigma, Σ, is used to denote the sum of a set of numbers.

- Example

Let be a function and are integers with . Then

- .
We say is the lower limit and is the upper limit of the sum.

We can replace the letter with any other variable. For this reason is referred to as a *dummy variable*. So

Conventionally we use the letters , , , for dummy variables.

- Example

Here, the *dummy variable* is , the *lower limit* of summation is 1, and the *upper limit* is 5.

- Example

Sometimes, you will see summation signs with no dummy variable specified, e.g.,

In such cases the correct dummy variable should be clear from the context.

You may also see cases where the limits are unspecified. Here too, they must be deduced from the context.

### Common summations[edit]