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In some cases where the direct comparison test is inconclusive, we can use the limit comparison test.
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If every term in one series is less than the corresponding term in some convergent series, it must converge as well. This notion is at the basis of the direct convergence test. Learn more about it here.
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When a series alternates (plus, minus, plus, minus,...) there's a fairly simple way to determine whether it converges or diverges: see if the terms of the series approach 0.
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Always start with this test.
If the terms of an infinite series don't approach zero, the series must diverge.

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