A sequence \{a_i\} is defined by a_1 = c for some c > 0 and a_{n+1} = a_n + \frac{n}{a_n}. Prove that \frac{a_n}{n} converges and find its limit.
A sequence \{a_i\} is defined by a_1 = c for some c > 0 and a_{n+1} = a_n + \frac{n}{a_n}. Prove that \frac{a_n}{n} converges and find its limit.