MATH 222 Study Guide - Midterm Guide: Jyj, Ratio Test, Absolute Convergence

• School: McGill University
• Department: Mathematics & Statistics (Sci)
• Course: MATH 222
• Professor: Christa Scholtz

Document Summary

Problem 1 consider the sequence {an} de ned recursively by: solutions a1 = 11, an+1 = 25 = 5, a2 = (a) limn an = 0. (b) limn an = 11. (c) limn an = 3. (d) limn an = 2. (e) the sequence does not converge to any real number. We nd that lim n an+1 = lim n an. X 2 2x 3 = 0. The sequence is strictly positive, so we choose x = 3. (cid:4) We can use l"hopital"s rule, or we can substitute the. 5! and now it is possible to calculate the limit. 3e2x 3 6x 6x2 4x3. = 2 + 0, lim x 0 and therefore the correct answer is (b). (cid:4) Problem 3 the interval of convergence of the power series (x 2)n is. (cid:88) x4 n n=1 (a) ( . 2, . 2) (b) [ . 2, . 2) (c) ( , ) (d) (1. 8, 2. 2) (e) [1. 8. 2. 2)