Hoi,

I was wondering if the following was true. I can't prove it...but it looks true

suppose $\displaystyle \lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^n| a_i-p| = \lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^n |b_i-q| = 0$

for series in $\displaystyle (a_i),(b_i) \subset \mathbb{R}$

Then $\displaystyle \lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^n|a_i b_i -pq| = 0$

Sounds like something that should be trivially true..but i have hard time showing it..