Discuss the convergence or divergence of the series .
This is another p-series, this time with , so we already know that this series diverges. However, let us look at the ratio test once more.
Again, the ratio test is inconclusive for a p-series. In fact, the ratio test is inconclusive for any p-series. The previous example showed a p-series which converged and this shows a p-series which diverges. The ratio test is inconclusive in both cases. The integral test works well for p-series but the ratio test does not.