Example: The series diverge.

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We will use the limit comparison test, together with the p-series test. First, note that

• 

Hence, by the limit comparison test, the two series

• 

and

• 1 /

have the same convergence behavior. But the second series is a p-series with p = 1/2, so it diverges by the p-series test. Hence, the original series also diverges.

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