Question 81
Let $a_{1}\gt 0$ and $a_{n+1}=a_{n}+\frac{n}{a_{n}}$ for $n \geq 1$. Prove that:
a) $a_{n} \geq n$ for $n \geq 2$;
b) the sequence $\left\{\frac{a_{n}}{n}\right\}_{n \geq 1}$ converges and find its limit.
a) $a_{n} \geq n$ for $n \geq 2$;
b) the sequence $\left\{\frac{a_{n}}{n}\right\}_{n \geq 1}$ converges and find its limit.