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Calculus BC: Series

Problems

The Comparison Test

Geometric Series and the Ratio Test

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/n 2 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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