CAS MA 124 Study Guide - Midterm Guide: Integral Test For Convergence, Convergent Series, Divergent Series

• School: Boston University
• Department: Mathematics & Statistics
• Course: CAS MA 124
• Professor: All

Document Summary

Ma 124 - fall "12 - exam 2b - answers. If the sum s10 of the rst 10 terms is used to estimate the value of s, nd the upper bound for the error r10 given by the integral test. Answer: note that k 1 0 < 1 < /2 sin(1/k) > 0 so the series has all terms positive. Sin(1/k) < 1 sin(1/k) k2 k2 (cid:88) sin(1/k) k2. Hence our series is less than a convergent series, so. 1 k2 converges since it is a p series with p = 2 > 1. (cid:88) converges by comparison test. sin(1/k) k2 k=1. Answer to b) on the next page: we have the following inequality for in nite series which converge by the integral test: (cid:90) (cid:90) 1. 1 x2 dx = lim b (cid:90) b. 1 x2 dx x 2 dx = x 1 =