Raymond W. Brink

A new integral test for the convergence and divergence of infinite series

A new sequence of integral tests for the convergence and divergence of infinite series has been developed by the author. Some of the tests of this sequence, and the principle by which they may be discovered will be set forth by him in another article. In the present paper it is his desire to give a central one of these tests, together with some of its applications. This particular integral test appears to play the same role when the ratio of successive terms is explicitly known, that the Maclaurin-Cauchy test plays when the individual term is explicitly known. In testing a series of the form