- #1

rainwyz0706

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(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!