Introduction
In this Section we consider power series. These are examples of infinite series where each term contains a variable, , raised to a positive integer power. We use the ratio test to obtain the radius of convergence , of the power series and state the important result that the series is absolutely convergent if , divergent if and may or may not be convergent if . Finally, we extend the work to apply to general power series when the variable is replaced by .
Prerequisites
- have knowledge of infinite series and of the ratio test
- have knowledge of inequalities and of the factorial notation.
Learning Outcomes
- explain what a power series is
- obtain the radius of convergence for a power series
- explain what a general power series is
Contents
1 Power series2 The radius of convergence
3 Properties of power series
4 General power series