If I conduct the ratio test for a series that is alternating in sign, and find that $\lim$ as $n$ goes to $\infty$ is $ >1$, is it mathematically correct to say that the entire series (including the alternating piece) is divergent? Or, must I conduct the alternating series convergence test?
2026-04-05 01:46:49.1775353609
If Ratio Test for an alternating series is Divergent, Must I run the Alternating series test?
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If the ratio test for the absolute values of the terms gives a limit $>1$, the terms cannot go to zero and therefore the original series diverges by the Divergence Test.