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10.4 Integral Test for Convergence

Definition: Integral Test

Let \(a_n = f(n)\).

If \(f(x)\) is positive, continuous, and decreasing on \([1, \infty)\), then:

  • \(\sum_{n=1}^{\infty} a_n\) and \(\int_{1}^{\infty} f(x) dx\) either both converge or both diverge.