Lesson 18a - Integral Test and P-test

Lesson 18a Integral Test and P-test

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Unformatted text preview: es (we know the numerator is not changing, but the denominator is getting larger) 2. an is always positive (as n is always positive, n2+1 will always be positive) 3. f(n) = an is a continuous function (there is no discontinuity in this function at all) This means we can compare the series to the integral: This means both the integral and the series converge by the Integral test! 1 (Note that the series does not dn ArcTan (n) 1 converge to this value, it simply n2 1 1 means it converges) 1 dn ArcTan () ArcTan (1) n2 1 244 1 Example 3 n Consider the following series: 2 n 1 n 1 1. an decreases. We must find the derivative to show that the following function decreases eventually: n f ( n) 2 n 1 (1)(n 2 1) (2n)(n) f ' ( n) 2 n2 1 1 n2 f ' (...
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

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