Module 9 :  Infinite Series, Tests of Convergence,  Absolute and Conditional Convergence, Taylor and Maclaurin Series
Lecture 26 :  Absolute convergence [Section 26.1]
 



Hence

.

Since, the series is convergent, the given series is also convergent.

In comparison test, or the limit comparison test, one needs to guess the convergent / divergence and then select an appropriate series to compare. Some convergence test which are more intrinsic are given next.

26.1.3 Theorem (The ratio Test):
 

Let be a series of positive terms such that

.

Then the following hold:

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