Ali and Haoyu are studying the sequence {an } generated as follows: an = 36 and an+1 = 12 -V144 - an, n = 0, 1,... Using mathematical induction, Ali and Haoyu have shown that . an is well defined for each n; . {an } is a non-increasing sequence with positive terms. (a) Ali then concludes that limn ->co an exists. Explain briefly why this limit exists. Equation Editor A - A- Ix BIUSX X Paragraph Font Size G body P Words: 0(b) Let L = limn->co an. Ali and Haoyu wish to compute the value of L. Help them by writing down the result in the box below. L = (c) Ali and Haoyu also would like to find the infimum (the greatest lower bound) of {an : n = 0, 1, . ..}. Let r = inf{an : n =0, 1, . . .}. Write down the value of r. (d) Finally, Haoyu challenges Ali to examine whether the series Zin-0 an is convergent or divergent. To do this, Ali first works out that lim an+1 an for some B > 1. Compute S and enter its value in the box below. B = Ali then tells Haoyu that _ an is convergent. Is this true or false? O True O False