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Engineering Mathematics, Volume I, Second Edition by Babu Ram

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EXAMPLE 1.57

Discuss the convergence of

  1. images
  2. images

Solution. (i) The nth term is

 

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Hence, by Gauss's Test, the series Σun converges.

(ii) For this series

 

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Therefore,

 

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and so the series diverges by Gauss's Test.

1.16 CAUCHY'S INTEGRAL TEST

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