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

If , then the series is convergent.

(ii)
 If or , then the series is divergent.
(iii)
 If , the series may converge or diverge.
 
26.1.4 Theorem (Root test):
 

Let be a series of positive terms and suppose that
                
Then the following hold:

(i)
 If , then the series is convergent.
(ii)
 If or, the series is divergent.
(iii)
 If , the series may converge or diverge.
 
26.1.5 Examples:
(i)
Consider the series
 

.
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