If you have a geometric alternating series, and you prove that the series is converging by doing geometric series test, and NOT alternating series test, then does that allow you to say that the series converges ABSOLUTELY?
Or should you do alternate series test also to say that it converges absolutely? I was confused because I know that ratio test and root test allows you to say that it converges absolutely without doing the alternate integral test.
What about the other tests like comparison tests and integral test?


If it is a geo alternating, then proof of the geometric convergence test is sufficent for absolute convergence.

Any test, and there are several, that says the series converges absolutely is sufficent: others are not required.

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