Lesson 19a - Integral Test Estimator

An isdecreasingeventually 2 an

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

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.

Ask a homework question - tutors are online