MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Consider the series n=1∑∞(−1)nn+1n.
Which statement correctly identifies the failed hypothesis of the alternating‐series convergence criteria and the resulting conclusion about the series?
(a) The monotone‐decreasing hypothesis fails, so the series diverges.
(b) The limit hypothesis fails, but because the series alternates, the nth–term divergence test is inconclusive.
(c) The limit hypothesis fails, so the series diverges by the nth–term test.
(d) Neither hypothesis fails, so the series converges.