There are five statements:(adsbygoogle = window.adsbygoogle || []).push({});

(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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Convergence test

**Physics Forums | Science Articles, Homework Help, Discussion**