10.4 The Divergence and Integral Test Math 6B Calculus II.

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Presentation transcript:

10.4 The Divergence and Integral Test Math 6B Calculus II

The Divergence Test

Harmonic Series

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.

The Integral Test In other words:

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.

p - Series

Estimating the Sum of a Series

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

Properties of Convergent Series