This article explores an improvement of D’Alembert’s ratio test, a fundamental criterion for determining the convergence or divergence of positive term series. Since the standard ratio test does not always give conclusive results, this work introduces an alternative approach using higher-order ratio tests. The second-order ratio test is presented and applied to examples such as the bi-geometric series to illustrate its effectiveness. Furthermore, the concept is extended to the ?$m$?-th order ratio test and compared with other known convergence tests, including Raabe’s test and Cauchy’s root test. The findings indicate that higher-order ratio tests provide a more powerful method for analyzing the convergence of series in mathematical analysis.

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