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In my Calc II class, we're just starting convergence tests and all the examples are very convinient and they work perfectly (obviously, since they are examples), but my professor couldn't really answer my question.

Is there a time, or some examples, where convergence tests will contradict each other? Like the ratio test says the series will converge, but the limit comparison test says it diverges, etc.

And if there are examples, how would I know which one is correct?

Again, sorry if this is trivial...

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    If you get far enough with math to reach analysis, you'll be able to see why the answer is no.2014-04-25

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They should never contradict one another. The worst that could happen is that one test is inconclusive while another definitively shows that the limit does or does not exist.

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    Ha, that's very true.2011-10-31