- Thread starter
- #1

- Apr 13, 2013

- 3,836

Let the sequence $(a_{n})$ with $a_{1}>0$ and $a_{n+1}=1+\frac{2}{1+a_{n}}$.Show that the subsequences $a_{2k}$ and $a_{2k-1}$ are monotonic and bounded.Find the limit $\lim_{n \to \infty} a_{n}$,if it exists.

Do I have to show separately that the two subsequences are monotonic and bounded??Or is there an other way to show it??Could I for example show that $a_{n}$ is monotonic and bounded??