The Relation Between the Root and Ratio Tests

摘要: then the series C a , converges. (For proofs, see Krantz [l]or Rudin [2].) Since limit in (1) is always greater than or equal to (21, root test stronger ratio test: there are cases which shows convergence but does not. (In fact, corollary of [l] .) We can illuminate relationship between these two tests with simple calculation: