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Compute S_15 with this recursion (make sure that you use an accurate value for pi). To analyze what happened in (a), consider the recursion S_n = 1 - 2n(2n - 1)/pi^2 S_n - 1, n = 1, 2,......, with S_0 = 2(1 - u), that is, the same computation with the starting value perturbed by one digit in the last place. Find a recursion for S_n - S_n. From this recursion, derive a formula for S_15 - S_15 i in terms of S_0 - S_0. Use this formula to explain what happened in (a). (c) Examine the "backwards" recursion S_n - 1 = (1 - S_n) pi^2/2n (2n - 1) starting with S_15 = 0. What is S_0? Why