Consider the sequence {In} generated by the rule I...\" = 1hr" + 1. (a) Let :1 = ; calculate the next 5 tenns and plot them. Does the sequence appear to converge? To what? (h) Explain Why it is reasonable to conjecture that lim In : X where IIH { X=V1+1+til+m. (c) Prove that {In} is an increasing sequence. (You can use induction or an},r other method.) (d) Prove that {31".} is bounded above by 2. (You can use induction or any other method.) (e) The last two parts implyr that {In} converges by the monotone convergence theorem. Find the limit X by using the same method as we used in class for the sequence, i.e. let In+1 = I\" = X in the iterating equation, and solve for X. Does the result agree 1Evith your estimate from {b}