Question 2
The real sequence $(x_n)$ is defined by
$$x_1=1,\qquad x_n=\frac{2n}{(n-1)^2}\sum_{i=1}^{n-1}x_i\quad(n\ge2).$$
Set $y_n=x_{n+1}-x_n$ for every positive integer $n$. Prove that $(y_n)$ has a finite limit as $n\to+\infty$.
$$x_1=1,\qquad x_n=\frac{2n}{(n-1)^2}\sum_{i=1}^{n-1}x_i\quad(n\ge2).$$
Set $y_n=x_{n+1}-x_n$ for every positive integer $n$. Prove that $(y_n)$ has a finite limit as $n\to+\infty$.