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Series converges implies $\lim{n a_n} = 0$
How do I show that the following:
If $ a_1 \geq a_2\geq ... \geq a_n\geq...$ and $\sum a_n$ converges then $\lim (n a_n) = 0$?
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Lonely Penguin
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3Since $a_n\to 0$ (this is necessary for the convergence of series), the monotonicity implies $a_n\ge 0$. With this additional condition, this is precisely the same question as Series converges implies $\lim{n a_n} = 0$. – Martin Sleziak Jan 14 '12 at 18:23
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thanks, that was the same question. – Lonely Penguin Jan 14 '12 at 18:28