Consider the infinite series
S=n=1∑∞(−1)n3nn2.
Answer the following questions.
(a) Determine whether the series S converges or diverges. Show all work leading to your conclusion.
(b) Decide whether the convergence found in part (a) is absolute or conditional. Fully justify your decision.
(c) State the numerical value of n→∞lim(−1)n3nn2 and explain how this limit supports your answer to part (b).