Question 1

1 Estimates of can be accelerated by writing its partial sums as 1 1 1 + n = 1 n(n + 1) and recalling that n = 1 n2 ( n + 1 ) n = 1 n = 1 N 1 1 = 1 - 1,000 1 n(n + 1) N+1 converges to one as /V -> co. Compare the estimate of using the sums 7 = 1 6 2 with the estimate using n = 1 1,000 1 1 + n2 ( n + 1 ) n = 1 1,000 O is more accurate. n = 1 1,000 H O 1+ is more accurate. n = 1 n2 ( n + 1 ) Both are equally accurate. It is not possible to tell which is more accurate.92 94 96 How many terms in cos(0) = 1 _ + _ _ + . . . are needed to approximate cos(1) accurate to an error of at most 0.00001? 2! 4! 6! N: Suppose that lim an + 1 00 = p. For which values of p must n - 00 4a converge? (Enter your answer using interval notation.) an n = 1 PE