Problem : Determine whether the series

   

converges or diverges.

The comparison test implies that the series diverges, since

≥    

and the harmonic series 1/n is known to diverge.

Problem : Determine whether the series

   

converges or diverges.

The n-th term of the series is equal to

= ≤    

Since the series 1/n2 converges, so does this series, by the comparison test.

Problem : Show that the series

   

converges.

This follows from the comparison test since

≤    

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