I have $\lim_{x_n\to\infty}=0$ and $\lim_{x_n\to\infty}x_{n+1}/x_n=L$. How do I show that $|L|<1$.
I tried to break it up and show that $L>-1$ and $L<1$, I let $\epsilon=|L|/2, \text{ and}\, \epsilon=|1-L|/2 $ but it didn't work out too well. I have too many case to work with.
Can anyone give me a better idea please?