The first series is shown to be divergent by comparing it to the harmonic series which is known to diverge.

The second series is shown to be divergent by using the root test.

The third series is convergent since it satisfies the ratio test. In addition, it is possible to find the sum of the series by using the sum of geometric progression formula.

The fourth series is shown to be absolutely convergent by the root test.

Apr 28th, 2015

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