Lesson 19a - Integral Test Estimator

# An isdecreasingeventually 2 an

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Unformatted text preview: ies that has the following properties: 1. an is decreasing (eventually) 2. an is always positive (eventually) 3. f(n) = an is a continuous function (eventually) f (n)dn If converges, then so does the series. 1 If we sum up to n terms then we have the error of stopping will be: n 1 ak dk Rn ak dk n Example 1 We have proved that this series converges by the integral test, now let us estimate after stopping after some terms. Determine the error if we stop after 3 terms: 1 n2 1 n 1 If we add the first three terms, we get: 111 4 2 5 10 5 According to the integral estimator, we get that the remainder R3 will be: ak dk Rn ak dk n 1 1 4 k 2 1dk Rn 3 k 2 1dk n 1...
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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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