# Is the following series convergent?

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Answer True/False to the statements.

I found that the limit is 0, and have tried ratio test (L=1) and comparison test, but am unsure how to prove it converges/diverges.

Answer True/False to the statements.

I found that the limit is 0, and have tried ratio test (L=1) and comparison test, but am unsure how to prove it converges/diverges.

##### 1 Answer

Jun 13, 2018

The series:

is divergent.

#### Explanation:

As:

we have that:

Based on the squeeze theorem we can therefore immediately determine that:

Consider now the series:

As:

based in the limit comparison test it must have the same character as the harmonic series that we know to be divergent.

But as:

then also the series:

is divergent by direct comparison.