Kummers Acceleration Method Suppose we wish to approximate S = n=1 1/n2. There is a
Chapter 10, Problem 93(choose chapter or problem)
Kummers Acceleration Method Suppose we wish to approximate S = n=1 1/n2. There is a similar telescoping series whose value can be computed exactly (Example 2 in Section 10.2): n=1 1 n(n + 1) = 1 (a) Verify that S = n=1 1 n(n + 1) + n=1 1 n2 1 n(n + 1) Thus for M large, S 1 + M n=1 1 n2(n + 1) 6 (b) Explain what has been gained. Why is Eq. (6) a better approximation to S than M n=1 1/n2? (c) Compute 1000 n=1 1 n2 , 1 + 100 n=1 1 n2(n + 1) Which is a better approximation to S, whose exact value is 2/6?
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer