There are five statements: (a) If n^2 an → 0 as n → ∞ then ∑ an converges. (b) If n an→ 0 as n → ∞ then ∑an converges. (c) If ∑an converges, then ∑((an )^2)converges. (d) If ∑ an converges absolutely, then ∑((an )^2) converges. (e) If ∑an converges absolutely, then |an | < 1/n for all suﬃciently large n. I suppose that a,d,e are true, not quite sure about b,c. Could anyone please give me some hints how to prove the statements or give some counter-example? Any help is greatly appreciated!