Module 9 :  Infinite Series, Tests of Convergence,  Absolute and Conditional Convergence, Taylor and Maclaurin Series
Lecture 26 :  Absolute convergence [Section 26.1]
26.1 More tests of convergence:
  We describe next a generalization of the comparison test. For that, we need the following result which allows one to compare terms of two sequences.
26.1.1 Lemma ( Limit Comparison):
 

 
26.1.2

Examples:

 

(i) Consider the series , where . Then

for every .

Since the series is divergent (example 25.1.4 (iv)), the series is also divergent for .

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