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Adding a series of numbers, called summation, is a simple example of computation. Below is a basic algorithm for summation:

Summation Algorithm:

Input:

Integer n, with n > 0

Output:

Variable t =1+2+3+...+n

Steps:

1. i = 0
2. t = 0
3. i = i + 1
4. t = t + i
5. if i ≥ n then we're done
6. go to step 3

The symbol Σ denotes summation and is used to represent calculations similar to the above.

Example: The simplest form of summation notation is

Given an integer n>0, the above notation represents the sum 1+2+3+...+n.

Example: We use sets to define a more general notion of summation. Let A = {1,2,3,...,n} with n>0. Then the previous example can also be written 

Notice how the more general notation for summation is similar to implicit notation for sets. In the above example, the dummy variable is i and the true/false statement is i∈A. The symbol Σ denotes the summation of all values of the dummy variable for which the true/false statement is true.

Example: Let A = {1,5,8,20}. Consider

This is 8+20 = 28.

Example: Let A = {4,8,12}. Consider

This is 4²+8²+12²+7² = 16+64+144+49 = 273.