CAS MA 124 Study Guide - Midterm Guide: Divergent Series, Alternating Series, Convergent Series

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

Document Summary

Ma 124 - fall "12 - exam 2a - answers: a) (4 points) true or false: Using comparison test we note: ln k 1 for k large. ln k k. (cid:88) k k=1 ln k k for k large. 1 k diverges since p series with p = 1. Our series bigger than a divergent series, hence diverges by comparison test. Note: one can also use the integral test to show this series diverges by showing the improper integral (cid:90) ln x x dx diverges. Answer to c) on next page: converges. = 0 lim x ln x x is indeterminate form. Applying l"hopital"s rule lim x ln x x. = lim x (ln x)(cid:48) x(cid:48) = lim x . = 0 ak+1 = ln(k + 1) (k + 1) = ak since if we let we have f(cid:48)(x) = f(x) = ln x x (1/x) x ln x x2 (ln x)(cid:48) x (ln x) x(cid:48) x2.