# Thread: proving that a function is monotonic and bounded..

1. ## proving that a function is monotonic and bounded..

in this link i written the question and how i tried to solve them

http://img504.imageshack.us/img504/7371/95405842kw4.gif

how to finish it??

2. Originally Posted by transgalactic
in this link i written the question and how i tried to solve them

http://img504.imageshack.us/img504/7371/95405842kw4.gif

how to finish it??
You need to prove that $\displaystyle a_n=\prod_{k=1}^{n}\frac{k+9}{2k-1}$ is both monotonic and bounded. Start with solving

$\displaystyle k+9<2k-1\implies 10<k$

So this tells us one thing since all the terms after ten are less than one we may say that $\displaystyle \sum_{k=1}^{n}\frac{k+9}{2k-1}<\prod_{k=1}^{10}\frac{k+9}{2k-1}=512$ and that $\displaystyle \forall{n}>10 a_{n+1}<a_n$

3. by saying that my series is smaller then 1
you are deciding that its descending.

why did you decided that its descending??
maybe its ascending and we should do bigger then 1
??

4. ok i understand the monotonic part

how to pove that this series is bounded?