The integral test for convergence is only valid for series that are 1) Positive: all of the terms in the series are positive, 2) Decreasing: every term is less than the one before it, a_(n-1)> a_n, and 3) Continuous: the series is defined everywhere in its domain. The integral test tells us that, if the integral converges, then the series also converges. But if the integral diverges, then the series also diverges.
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