  The classical D'Alembert's Ratio Test is a powerful test that we learn from
calculus to determine convergence for a series of positive terms. Its range of
applicability and ease of computation makes this test extremely appealing.
However, it admits an inconclusive case when the limiting ratio of the terms
equals 1. Several series tests like Raabe's and Gauss' Tests have been proposed
in order to address this case. These tests were also generalized by Kummer
through Kummer's Test. More recently, a Second Ratio Test was constructed that
similarly possessed an inconclusive case. This article will present a survey of
existing series tests. Secondly, it will introduce an extension of Raabe's Test
to the Second Ratio Test. Thirdly, other extensions of classical tests such as
Gauss' Test and Kummer's Test are proposed. Finally, it will also present
proofs for the aforementioned tests and a brief application of the Second
Raabe's Test.
