MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
A student knows that ∑an is conditionally convergent. Which statement about rearrangements of the terms is most accurate?
(a) Every rearrangement converges to the same value because the series still converges.
(b) A rearrangement can at most change the sum by a finite constant, never to an entirely different value.
(c) Some rearrangements can change the value to which the series converges.
(d) Any rearrangement must diverge because conditional convergence is fragile.