3. A sequence {an} is defined recursively by a1 = x/i and a2 = w/ 2 + an. (a) Prove, by induction, that {an} is an increasing sequence. (b) Prove, by induction, that {an} is bounded above by 3. (c) Apply the Monotone Sequence Theorem to prove that limnuoo an exists, and therefore {an} con- verges. (You do NOT need to prove the limit exists using 5's and N '5 since you can quote the Monotone Sequence Theorem.) (d) For the purpose of this question you may assume, without proof, that if {an} converges, then lim,H00 an\" exists and is equal to limn_>00 an. Using this fact, find the limit limnaoo an