MATH1051 Chapter Notes - Chapter 8: Product Rule, Differentiable Function, Antiderivative
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Chapter 8 power series and taylor series. A power series is a series of the form: This is a power series about a (or centred about ). variable. The ratio test is generally useful for dealing with these. For example, if you(cid:495)re asked to the following series converges (the interval of convergence): determine for which values of and are fixed, while is. This cancels to (cancelling the powers first, and dividing the rest by the highest power of denominator): in the. However, the ratio test hasn(cid:495)t given any information about those endpoints. This value is called the radius of convergence. The interval of convergence is the interval which consists of all values of converges. for which the series. Given a function it is sometimes possible to expand as a power series: If you assume that defined at and all its derivatives are.
