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Module 9 : Infinite Series, Tests of Convergence, Absolute and Conditional Convergence, Taylor and Maclaurin Series

Lecture 27 : Series of functions [Section 27.1]

	Then
(i)	The function has an anti derivative given by
	where is an arbitrary constant, and the series on the right hand side has radius of convergence .
(ii)	For ,
	where the series on the right hand side is absolutely convergent.
27.1.9	Example :
(i)	Consider the power series
	By the ratio test, for every Hence, the series is absolutely convergent for every . Let