# convergence of sum

• Nov 6th 2012, 01:24 PM
Dinkydoe
convergence of sum
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.
• Nov 6th 2012, 01:44 PM
awkward
Re: convergence of sum
Suppose $a_n = 2$. Then what?
• Nov 6th 2012, 01:54 PM
Dinkydoe
Re: convergence of sum
ehm...ur right. its not true XD