Question 1
Define $x_1=1$ and
$$x_{n+1}=x_n+3\sqrt{x_n}+\frac n{\sqrt{x_n}}\quad(n\ge1).$$
a) Prove $\lim_{n\to\infty}n/x_n=0$.
b) Find $\lim_{n\to\infty}n^2/x_n$.
$$x_{n+1}=x_n+3\sqrt{x_n}+\frac n{\sqrt{x_n}}\quad(n\ge1).$$
a) Prove $\lim_{n\to\infty}n/x_n=0$.
b) Find $\lim_{n\to\infty}n^2/x_n$.