- #1

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Proof that:

[tex]\frac{n}{n+\sqrt{n}} \leq u_{n} \leq \frac{n}{n+1} [/tex]

Ok, I've been working on that problem for about two hours now and I still don't have a clue how to proof this inequality.

I guess it should be done by induction, but I have problems with the series, because I don't know how I could possibly pass from n to n+1, since the variable n is on the denominator.

Perhaps there is a pretty easy solution to this problem, but any help would be welcome!

(I'm sorry that I don't post my attempts at a solution, but I have to much of them and I don't believe that there is anything really productive

Thanks in advance :)