# Math Help - Prove that this converges

1. ## Prove that this converges

Let [a,b] be a closed interval in $\mathbb R$, and suppose that { $\ s_n$}, $\ n \geq 1$ is a sequence within [a,b]. Prove that the sequence { $s_n/n$}, $\ n \geq 1$, converges.

Anyone know how to do this problem? thanks in advance guys.

2. Originally Posted by Cato
Let [a,b] be a closed interval in $\mathbb R$, and suppose that { $\ s_n$}, $\ n \geq 1$ is a sequence within [a,b]. Prove that the sequence { $s_n/n$}, $\ n \geq 1$, converges.

Anyone know how to do this problem? thanks in advance guys.
note that the $s_n$'s are bounded.

3. We have
$\frac{a}{n}\leq \frac{s_n}{n}\leq \frac{b}{n}$
then use squeeze theorem

4. Why $a/n$ and $b/n$

5. Originally Posted by Cato
Why $a/n$ and $b/n$
it is within the interval [a,b]. so the smallest an element of the sequence can be is a, while the largest it can be is b

6. Thanks guys