## power series

A power series has the form:

where both

*c*and*a*are constants.*c*must be a nonzero number that is negative or positive, but*a*may be zero, positive, or negative.*x*may have a constant inside of the power, such as (2x)^n or (3/4 * x)^n. Note that*c*is not raised to the power*n*.## uses and relations to other topics

A power series is much like Taylor/Maclaurin series in that it is used to find the graph of an unusual function. The power series is a type of convergence test as well - if | x | > 1, it will not converge. These functions must have the form:

## geometric series

Geometric series are very similar to power series - the only difference is that

*x*(or*x*-*a*) is replaced by*r*, where | r | < 1. Unlike power series (which diverge), geometric series converge. The limit of the geometric series is c / (1 - r). If the sum of the polynomials does not go to infinity, but instead goes to a numerical value, useto find the sum of the polynomials.

Note: the limit and sum equation only work with geometric series, not power series.

Note: the limit and sum equation only work with geometric series, not power series.

## uses and relations to other topics

Geometric series are used to express repeating decimals as fractions!