Consider the series
n=1∑∞n+12n.
Which statement provides the most direct justification for its convergence or divergence?
a) It converges absolutely by the ratio test.
b) It converges by the alternating series test because the terms decrease and alternate in sign.
c) It diverges because n→∞limn+12n=0.
d) It converges conditionally by comparison with the harmonic series since n+12n<n1.