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

The function is differentiable on the interval . Further the series

also has radius of convergence , and .

The function has derivatives of all orders and .   

27.1.8

Theorem (Integration of power series):

 

Let

be a power series with non-zero radius of convergence and let

.
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