Module 9 :  Infinite Series, Tests of Convergence,  Absolute and Conditional Convergence, Taylor and Maclaurin Series
Lecture 26 :  Absolute convergence [Section 26.1]
5.

Canchy's Condensation Test

 

Let be a decreasing sequence of positive terms. Let

               

Prove the following:

(i)
 For every , 
              
(ii)
 Deduce that the series    is convergent if and if the series  is convergent.
 
6.
 Using exercise (5), deduce that the series
                

are convergent for and divergent for .

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