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

Thus, the series is divergent by the root test.

We close this section by another test.

26.1.6

Theorem (Integral Test):

 

Let be a positive continuous decreasing function with
            
Then either both
            
converge or diverge.

 
26.1.7 Examples:
(i)
p-Series:
 

Consider the series


Obviously, the series is divergent for , as for even . If we consider the function

,
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