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Possible Duplicate:
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 $\lim (n a_n) = 0$?

Thanks.

  • 3
    Since $a_n\to 0$ (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 $\lim{n a_n} = 0$](http://math.stackexchange.com/questions/4603/series-converges-implies-limn-a-n-0).2012-01-14
  • 0
    thanks, that was the same question.2012-01-14

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