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10.4 The Divergence and Integral Test Math 6B Calculus II

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The Divergence Test

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Harmonic Series

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The Integral Test Suppose f is a continuous, positive, decreasing function on and let a k = f (k). Then the series is convergent if and only if the improper integral is convergent.

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The Integral Test In other words:

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p - Series Q: Does the series converge? (p is constant) A:It depends on what p is, lets look at p >1, p < 1, p = 1.

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p - Series

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Estimating the Sum of a Series

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Furthermore, the exact value of the series is bounded as follow:

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Properties of Convergent Series

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Goal: Does a series converge or diverge? Lecture 24 – Divergence Test 1 Divergence Test (If a series converges, then sequence converges to 0.)

Goal: Does a series converge or diverge? Lecture 24 – Divergence Test 1 Divergence Test (If a series converges, then sequence converges to 0.)

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