Lesson 18a - Integral Test and P-test

An f ndn 1

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Unformatted text preview: the box an (which will be f(n)) will be smaller than the value of the integral: This means that adding the areas: n a2 a3 a4 ...an f (n)dn 1 This is almost the series, but we are missing the first term: n a1 a2 a3 a4 ...an a1 f (n)dn 1 Integrals and Areas n a1 a2 a3 a4 ...an a1 f (n)dn 1 This means that our partial sum from 1 to n is: n S n a1 f (n)dn 1 If the integral is continuous and converges to a number, this means we have (going to infinity) lim S n a1 f (n)dn L n 1 Since the numbers are strictly decreasing, and are positive, we have that the Sums Sn are going to get larger and larger, but we are bounded above by...
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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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