A student approximates the sum of an alternating series whose positive term…
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
A student approximates the sum of an alternating series whose positive term magnitudes decrease monotonically to 0 by adding terms until the first neglected term is less than 0.001.
Which statement best describes the accuracy of the student’s approximation?
(a) The magnitude of the error is guaranteed to be less than 0.0005.
(b) The magnitude of the error is guaranteed to be less than 0.001.
(c) The magnitude of the error could be as large as 0.001.
(d) No conclusion about the error can be drawn without knowing additional information.