A series is closely related to the sum of numbers. It is actually used to help add numbers; therefore, in a sequence it can be the indicated sum of that sequence. In general, the idea is to start with a number, then do something to that number to get the next number, then do the same to that number to get the next number, and so on. For example, a finite series with six terms is 2 + 4 + 6 + 8 + 10 + 12, in which 2 is added to each number to get the next number. An example of an infinite series is one with the notation 1/2ⁿ, with n ≥ 1, or ½ + 1/4 + 1/8 + … (and so on).

To see a series written in notation, if set {x_n} is a sequence of numbers being added, and set s₁ = x₁, then s₂ = x₁ + x₂; s₃ = x₁ + x₂ + x₃; and so on. And for n ≥ 1, a new sequence is made, {s_n}, called the sequence of partial sums, or s_n = x₁ + x₂ + … + x_n