In this Section we examine an important example of an infinite series, the binomial series:
We show that this series is only convergent if and that in this case the series sums to the value . As a special case of the binomial series we consider the situation when is a positive integer . In this case the infinite series reduces to a finite series and we obtain, by replacing with , the binomial theorem :
Finally, we use the binomial series to obtain various polynomial expressions for when is ‘small’.
- understand the factorial notation
- have knowledge of the ratio test for convergence of infinite series.
- understand the use of inequalities
- recognise and use the binomial series
- state and use the binomial theorem
- use the binomial series to obtain numerical approximations