I tried the ratio test and I got 1, which means inconclusive. What can I do to tell whether it is converging or diverging?
In this case oscillating and alternating are synonomous. And secondly no that is completely incorrect. Holistically being alternating greatly increases the chances a series converges. It mus satisfy much less stringent requirements. Do you know the Alternating Series Test (Leibniz's Criterion)?
Pauls Online Notes : Calculus II - Alternating Series Test
you're not an "online" student, are you?