Let r E R satisty |r| < Let An = 5 Bn = 1 – r" , and Cn 2 - n 10 Note: The aim of this question is to determine whether the above sequences are increasing, decreasing, or bounded. A. The sequences An, Bn, and Cn converge to 5,0, and o∞ , respectively B. One of the sequences is decreasing, two increasing, and two are bounded C. The sequences An, Bn, and Cn converge 5, 0, and 0, respectively D. The three sequences are decreasing and two of them are bounded E. The three sequences are all increasing F. Two of the sequences are decreasing, one is increasing and one is bounded

Can use basic facts about sequences.

10. Let {an}, {bn} and {cn} be sequences of real numbers. Which of the following statements are true? I. If {an} is convergent and {bn} is bounded, then {a„bn} is convergent. II. If lim an = L and lim b, = 0, then n-00 lim anbn = 00. n-00 III. If a, #0 for all n e Z+ and lim n→∞ An 0, then %3D lim an = 00. n-00 IV. If lim an = 0 and {bn} is bounded, then n-00 lim anbn = 0. n00 V. If b, < an < Cn for all n e Zt, {bn} and {cn} are convergent, then {an} is also convergent. VI. If {an} is unbounded, then {an} is divergent. (a) I, II (b) I, IV (c) IV, VI (а) , II, V (е) 1, IV, V

Let f be a real-valued function with domain R defined by f(x) = x2.  Define a sequence (s1, s2, s3, ...) by s1 = b and sj = f(sj-1), for j = 1,2,3,4...   a) assume that b=1, and find a formula for sn. b) assume that b=3, and find a formula for sn. c) prove the conjecture in part (b).