Let S=∑n=0∞3(52)n.
Complete the following tasks to approximate S to within 0.0001.
(a) Show that the difference between two successive partial sums, ∣SN+1−SN∣, equals 3(52)N+1. Explain why this difference can be used as an upper bound on the absolute error ∣S−SN∣.
(b) Determine the least integer N such that using SN guarantees an approximation accurate to within 0.0001.
(c) Calculate SN found in part (b) and record the value to five decimal places.