4.2. Convergence Tests

Integral Test

Suppose that f(x) is positive, continuous, decreasing function on the interval [N, ). Let a n = f(n). Then
converges if and only if converges
Note that this test is much different from all the others. We have not yet formally introduced the concept of an Integral - or even of a continuous function - so that we can not prove this test here. However, for completeness it is included as a test that is sometimes useful to apply.
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