EXAMPLE 1.57

Discuss the convergence of

  1. images
  2. images

Solution. (i) The nth term is

 

images

 

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

(ii) For this series

 

images

 

Therefore,

 

images

 

and so the series diverges by Gauss's Test.

1.16 CAUCHY'S INTEGRAL TEST

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