I'd like your help with this:
The sequence $a_{_{n}}$ applies these condition:
$a_{_{n}}> 0$ for every $n \in \mathbb{N}$
$\lim_{n\to \infty }\frac{a_{n+1}}{a_{n}}< 1$.
I need to prove that $a_{n}$ is convergent, and it's limit is 0.
I tried to work with the fact that $a_{_{n}}> 0$ and (not successfully) show that $a_{n}> a_{n+1}$, and than to conclude what I need.
Thanks