Which of the following sets of conditions must be verified before the…
MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Which of the following sets of conditions must be verified before the alternating–series error bound can be invoked to estimate the remainder of a Taylor approximation?
(a) The terms of the series alternate in sign and approach 0, but they need not decrease in magnitude.
(b) The terms of the series are all positive, decrease in magnitude, and approach 0.},{
(c) The terms of the series alternate in sign, decrease in magnitude, and approach 0.},{
(d) The terms of the series alternate in sign, and their derivatives are bounded on the interval of interest.