limit superior and limit inferior

Quote:

Originally Posted by summerset353

I dont understand limit superior and limit inferior. I know what the definitions are but I would not know how to apply it in an example since my teacher did not explain how to go about that. How would I find the limit superior and limit inferior of {(n/3)-[n/3]}?

I'll show you one part. You show me another. I assume that this is $a_n=\frac{n}{3}-\left\lfloor \frac{n}{3}\right\rfloor$ . Clearly, we have that $a_n\geqslant 0$ and so $\liminf\text{ }a_n\geqslant 0$ but considering that $a_{3n}=0$ we see that $\liminf\text{ }a_n=0$ .