Prove that this converges

**Cato** · October 8th 2008, 07:30 PM

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.

**Jhevon** · October 8th 2008, 07:37 PM

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.

**watchmath** · October 8th 2008, 07:39 PM

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

**Cato** · October 8th 2008, 08:09 PM

Why $a/n$ and $b/n$

**Jhevon** · October 8th 2008, 08:11 PM

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

**Cato** · October 8th 2008, 08:23 PM

Thanks guys

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