MAT137Y1 Midterm: 2009 Summer Test 3 solution

• School: UTSG
• Department: Mathematics
• Course: MAT137Y1
• Professor: N/ A

Document Summary

Term test 3 solutions, july 2009: state whether the sequence converges or diverges. If it converges, nd the limit of the sequence. (a) an = ( 1)n n. The sequence an = ( 1)n n is unbounded: n as n . [7%] (b) an = ln(n + 1) ln(n) The sequence converges to zero: an = ln(n + 1) ln(n) = ln( n + 1 n. We can write down the values of this sequence: {an} = {cos( ), cos(2 ), cos(2 ), cos(3 )} = { 1, 1, 1, 1, 1} and witness that an fails to converge to a limit. We will show that an is bounded below by zero, and above by a sequence which. 1 2 (n 3)(n 2)(n 1) n since all the terms between 23 and are less than 1. 2 (cid:180)(cid:179) 2 (cid:179)2 (cid:180)(cid:179) 2 (cid:179)2 (cid:179) 2. = 23 (cid:180)(cid:179) n (cid:180) n n 2 n 1.