MATH 3100 Midterm: MATH 3100 UGA SampleExam3_Version2

• School: University of Georgia
• Department: Mathematics
• Course: MATH 3100
• Professor: All

Document Summary

Good luck: (15 points) (a) carefully state the de nition of what it means to say that an is convergent. an is convergent and bn is divergent (not convergent), Pn=1 (b) use this de nition to prove that if then (an + bn) is divergent. Pn=1 (c) prove that if 0 an cn and cn is convergent, then. Pn=1: (15 points) (a) show that if lim n . Nan = 2, then (b) find all x r for which. Pn=1 (c) find a sequence {an} so that an diverges. 2x + 1 x2 + 1 (b) prove that if a function f : r r is continuous at x0, then lim n . Use this to show that f (xn) = f (x0) for all sequences g(x) =(cos(x 2) A sequence {bn} with 0 bn . 1 n for each n n, but for which ( 1)n+1bn diverges.