MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
The series n=1∑∞(−1)n+1n31 converges.
Use the following tasks to approximate its sum to within 0.0001.
(a) Determine the least positive integer N such that the magnitude of the error made by using SN to approximate the sum is less than 0.0001. Show analytic reasoning that leads to your value of N. Do not evaluate any partial sums in this part.
(b) Compute SN found in part (a) to six decimal places.
(c) State how many correct decimal digits your approximation from part (b) guarantees for the exact sum of the series. Explain your reasoning.