- #1
rainwyz0706
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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!
(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!