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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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1Series 1.1Alternating Series 1.2Absolute Convergence 1.3 Rearrangement of Series. 1.4Comparison Tests 1.5Ratio and Root Tests 1.6Other tests MAT 127 2.0.

1Series 1.1Alternating Series 1.2Absolute Convergence 1.3 Rearrangement of Series. 1.4Comparison Tests 1.5Ratio and Root Tests 1.6Other tests MAT 127 2.0.

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