LING 1100 Midterm: 2007CTest4-sol.pdf

• School: Carleton University
• Department: Linguistics
• Course: LING 1100
• Professor: Ida Toivonen

Document Summary

Math2007c - test 4 - 19:35 -20:25, mar 19, wednesday. Closed book, non-programmable calculators are allowed: (4. 5 points) determine whether the following sequence converges or diverges. Justify your answer. (a) an = 5 + 2n. 3n (b) bn = 32n ( 7)n (c) cn = ln n n . Solution: (a) lim n an = lim n (5 + (b) diverges. 3n ) = 5, since an = 5 + (cid:12)(cid:12) 9 7 (cid:12)(cid:12) > 1. 3 (cid:12)(cid:12) < 1. (c) by l"hospital"s rule, lim x ln x x. = 0 , lim n cn = 0: (5 points=1+2+2) find the sum of the following series: (a) 1 n(n + 1) n=4 n (n)(n + 1) = 1:75: (5. 5 points=1+2. 5+2) determine if the following series converges or diverges: (a) n=1 n + 1 n + 100 (b) n=3. Solution: (a) note that lim n (b) we use integral test.