Question 107
A sequence $(x_n)$ is defined as follows $x_1 = 1$ and $x_{n+1} = x_n + 3\sqrt{x_n} + \frac{n}{\sqrt{x_n}}$ for all positive integers $n$.
a) Prove that $\lim_{n \to +\infty} \frac{n}{x_n} = 0$.
b) Find the limit $\lim_{n \to +\infty} \frac{n^2}{x_n}$.
a) Prove that $\lim_{n \to +\infty} \frac{n}{x_n} = 0$.
b) Find the limit $\lim_{n \to +\infty} \frac{n^2}{x_n}$.