Limit of the greatest integer number

1. Jan 27, 2012

LikeMath

Hi there,

It is clear that

$\lim_{n\to\infty }\frac{1}{n}\left[\frac{n}{3}\right]=\frac{1}{3}$.
But the problem that I could not get a formal proof!

Thank you.

2. Jan 27, 2012

micromass

Try the squeeze theorem.

3. Jan 27, 2012

LikeMath

Yes, Thank you.