Although as , so that the denominator is smaller than , the denominator of the harmonic series, and hence, the terms of this series will be greater than the terms of the divergent harmonic series. This observation suggests the Limit-Comparison test, with the harmonic series as the comparison series. The relevant calculation is then
By part (3) of the Limit-Comparison test
, if the comparison series diverges, so also the given series diverges.
Alternatively, part (1) of the Limit-Comparison test with the divergent -series () as the comparison series also establishes the divergence of the given series because = .