Module 9 :  Infinite Series, Tests of Convergence,  Absolute and Conditional Convergence, Taylor and Maclaurin Series
Lecture 27 :  Series of functions [Section 27.1]
(ii)

The power series is a power series centered at . For every fixed value of , this can be treated as a geometric series with common ratio

 

Thus, for a particular , it will be convergent if ,and its sum is

Hence,

(iii)
 Consider the series
 

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