MATH 131 Final: MATH 131 UMass Amherst 131f17 Final Exam
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Problem 1 (5 points each) determine whether each sequence a n converges or diverges. If it converges, find the limit. (a) a n n2 3. 2n 1 lim n n2 3. So the sequence diverges. n n 3. 2 1 n (b) a n n e n. Hence, lim n n e n 0. lim x x e x lim x . Problem 2 (5 points each) use the squeeze theorem to show that the sequence converges to 0 : a n sin n n. 1 n 1 lim n sin n n 0, lim n n. Hence, by the squeeze theorem, we conclude that lim n sin n n.
