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

To find the value of for which the series will be convergent, we apply the ratio test. Since

the series is absolutely convergent for with , i.e.,

absolutely convergent for

And the series is divergent if

For , the series is

which is absolutely convergent. Also for , the series is convergent. Hence, the series has radius of convergence , with interval of convergence .

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