Geodesic
A note on Cauchy's root test
Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 151-154

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Throughout this note we deal with a series Σan of positive terms. The following tests for the convergence of this series are well-known.Test 1. (Ratio test). LetThen, if K < 1, Σanconverges, while if K > 1, Σandiverges.Test 2. (Root test). LetThen, if K < 1, Σanconverges, while if K > 1, Σandiverges. 
Murphy, I. S. A note on Cauchy's root test. Glasgow mathematical journal, Tome 17 (1976) no. 2, pp. 151-154. doi: 10.1017/S0017089500002883
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