# proving that a function is monotonic and bounded..

• Dec 9th 2008, 11:24 AM
transgalactic
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??
• Dec 9th 2008, 10:23 PM
Mathstud28
Quote:

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 $a_n=\prod_{k=1}^{n}\frac{k+9}{2k-1}$ is both monotonic and bounded. Start with solving

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

So this tells us one thing since all the terms after ten are less than one we may say that $\sum_{k=1}^{n}\frac{k+9}{2k-1}<\prod_{k=1}^{10}\frac{k+9}{2k-1}=512$ and that $\forall{n}>10 a_{n+1}
• Dec 9th 2008, 11:33 PM
transgalactic
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
??
• Dec 10th 2008, 11:32 AM
transgalactic
ok i understand the monotonic part

how to pove that this series is bounded?