Given a sequence $\{a_n\}$, with $n\geq1$, where $a_{1}=4,$ and $a_{n+1}=\sqrt{a_{n} +20}.$ Prove via induction that, for all $n \geq 1$, $a_{n+1}>a_{n}.$
- Apparent Convergence
The sequence appears to be increasing, and possibly bounded at 5. How may I show convergence, and find its limit.
- Regarding Notations
Additionally are there any beginners guide on using appropriate notations?
Thank you for your assistance.