Hi,

I have to show that, given a sequence (x_n) of real numbers with the property $\displaystyle |x_n|\geq n$ for infinitely many n, the sequence

$\displaystyle a_n=\frac{1}{n}\sum_{i=1}^n x_n$

does not converge. I tried a lot, but was not very successful.

Can I somehow show that $\displaystyle a_n$ can't be a Cauchy sequence?

Any ideas would be appreciated.

Thank you,

mili03