# The Ratio Test The ratio test is an infinite series convergence test that should be used when dealing with products (especially factorials), exponents, or powers. If dealing with $\sum_{j=0}^\infty a_j$, determine $L$: $L = \lim_{j \to \infty} \left | \frac {a_{j+1}} {a_j} \right|$ If $0 \le L < 1$: the sum converges. If $L > 1$: the sum diverges. If $L = 1$: the test is inconclusive.