Module 9 :  Infinite Series, Tests of Convergence,  Absolute and Conditional Convergence, Taylor and Maclaurin Series
Lecture 26 :  Conditional convergence [Section 26.2]
26.2.4

Theorem:

  If a series is absolutely convergent, then it is also convergent.
  Proof
 

Let

Then

Thus,

Since is convergent, by comparison test, is also convergent. Hence, by theorem 25.2.4, since

 
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