ECON 4350 Midterm: ECON 4350 UGA 4350.hexam1.16
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Good luck: (12 points) determine which of the following sequences converge and which diverge. Find the value of the limit for those which converge. Be sure to give a short justi cation in each case by indicating any limit laws, theorems, or special limits used. (a) an = ( 1)nn (b) bn = 2n n2 + 2n (c) cn = ( 1)n (d) dn = n + 1 n. 1 n: (14 points) (a) let {xn} be a sequence of real numbers. Carefully state the de nition of lim xn = l. n (b) use your de nition above to prove that lim n (c) use your de nition above to prove that if is bounded (but not necessarily convergent), then lim. 2n + 1 n + 2 xn = 0 and {yn} xnyn = 0. n lim n : (12 points) let x1 = 0 and xn+1 =
