Module 9 : Infinite Series, Tests of Convergence, Absolute and Conditional Convergence, Taylor and Maclaurin Series
Lecture 27 : Series of functions [Section 27.1]
This is a power series centered at . For its convergence, let us apply the limit ratio test. Since
the series is convergent absolutely for ,and is divergent for other values of
For , the series is ,
which is a divergent series. Also for , it is the alternating harmonic series. Thus, the given power series is convergent with domain of convergence being the interval
The domain of convergence if a power series is given by the following theorem.
. For its convergence, let us apply the limit ratio test. Since 
,and is divergent for other values of 
, the series is 
, 
, it is the alternating harmonic series. Thus, the given power series is convergent with domain of convergence being the interval 
