Use the quotient test, You'll obtain that for the series is convergent if and divergent if . For is divergent (compare for example with ).
Of course, the ratio test can be used here...
The series converges when this limit is . So we need to evaluate the values of for which this ratio is , and since ...
So the series is convergent when .
Since the ratio test fails when the limit is , you need to substitute into the original series and test the convergence of the series for that value.