MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Consider the series k=1∑∞k(k+3)3. Which of the following best describes its behavior?
(a) It diverges because the limit of its terms is non-zero.
(b) It converges because its partial sums telescope to a finite limit.
(c) It converges because it is a p-series with p>1.
(d) It diverges because a comparison with the harmonic series shows its partial sums grow without bound.