convergence of sum

**Dinkydoe** · November 6th 2012, 01:24 PM

Hoi, is there a way we can conclude that

$\lim_{n\to\infty}\frac{a_1+\cdots + a_n }{n} = \infty$ from the assumption that for some positive constant $K$

$\lim_{n\to\infty}\frac{\log(a_1)+\cdots \log(a_n)}{n} = K$

I need it for something, but i'm not even sure if it's true...?

The $a_n\geq 1$ are positive integers.

**awkward** · November 6th 2012, 01:44 PM

Suppose $a_n = 2$ . Then what?

**Dinkydoe** · November 6th 2012, 01:54 PM

ehm...ur right. its not true XD

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