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??
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 $\displaystyle \forall{n}>10 a_{n+1}<a_n$