Which statement best describes the convergence of the series n=0∑∞(−1)n(n+2)!(n+1)!?
a) It converges conditionally; the alternating series converges, but the series of absolute values diverges.
b) It converges absolutely; applying the ratio test gives a limit of 0, so the series converges.
c) It diverges; simplifying the factorials gives the harmonic series, which is known to diverge.
d) It converges to exactly 1 because the factorial terms create a telescoping pattern.