Originally Posted by

**Joel24** Ok, thank you. :)

In the seminars, we haven't been told that $\displaystyle lim_{n \to \infty} \left(\frac{a_n}{n} \right) = 0 $ if the sequence is bounded. As obvious as it is. :p

So do you think it would be more 'rigorous' if I said that since $\displaystyle a_n $ is bounded, there exists an $\displaystyle M$ such that $\displaystyle | a_n | \leq M $

Then I can show that $\displaystyle lim_{n \to \infty} \left(\frac{M}{n} \right) = 0 $ and $\displaystyle lim_{n \to \infty} \left(\frac{-M}{n} \right) = 0 $. Since $\displaystyle -M \leq a_n \leq M$, $\displaystyle \forall n $ then by the sandwich theorem, $\displaystyle lim_{n \to \infty} \left(\frac{a_n}{n} \right) = 0 $

That is excellent.

Is that fine, in your opinion, or unnecessary?

Thanks.