The sum has been computed to more than 100 million digits. The first 30 digits are S

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The sum 00 S s =  k=1 -3has been computed to more than 100 million digits. The first 30 digits are S = 1.202056903159594285399738161511. Approximate S using Kummer’s Acceleration Method of Exercise 91 with the similar series 00 n=1 (n(n + 1)(n + 2))^

and M = 500. According to Exercise 60 in Section 10.2, the similar series is a telescoping series with a sum of 1/4.


Data From Exercise 91

Suppose we wish to approximate 00 S s =  1?. n=1There is a similar telescoping series whose value can be computed exactly (Example 2 in Section 10.2):

Example 2 Section 10.2EXAMPLE 2 An 80-kg skydiver steps out of an airplane. (a) What is her terminal velocity if k = 8 kg/s? (b)

(a) Verify that Thus for M large, n=1 1 n(n + 1) 1 00 1 S =  MGA + 1) +  (1-+ 13) n(n n(n n=1 n=1 M s~1+; n=1

(c) CAS Compute 1000 n=1 1 + 100 1 n(n + 1) n=1 Which is a better approximation to S, whose exact value is /6?

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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