A test for convergence or divergence of an infinite series $\sum a_n$, due to D’Alembert. If the ratio $\left|\frac{a_{n+1}}{a_n}\right|\to k\text{as}n\to \infty$ then when k<1 the series converges absolutely, and for k>1 the series diverges. If k = 1, the ratio test is not sufficient to determine whether it converges. For example, k = 1 for both the series $\sum 1/n$ and $\sum 1/n^2$, but the first series diverges whereas the second converges.