# Series

A series is the operation of adding an infinite number expressions together. A series is denoted using the summation operator and the index variable k.

The partial sum of a series is denoted as and represents the summation of the first terms of the series. Shown below are the first 3 partial sums of a series and as well general form of .

There are two sequences associated with every series that can easily be confused with one another. The first is the sequence of -th terms.

The second sequence is the sequence of partial sums where each partial sum represented the sum of the first terms of the series.

### Example: Sum of Counting Numbers

For example, the series which corresponds to the natural numbers is represented by the expression below.

The sequence of -th terms is represented as

The sequence of partial sums is represented as

## Geometric Series

The variable represents the ratio between the terms of the series and represents the first term of the series.

## Power Series

A power series centered at is a series in the form below. The terms represent the ceffecients of the series.