# The Root Test The root test is an infinite series convergence test that should be used when dealing with expressions like $(a_j)^j$, and the limit of $a_j$ is known. If dealing with $\sum_{j=0}^\infty a_j$, determine $L$: $ L = \lim_{j \to \infty} \sqrt[j] {|a_j|} $ If $0 \le L < 1$: the sum converges. If $L > 1$: the sum diverges. If $L = 1$: the test is inconclusive.