Limit of a sequence : $x_n = \frac{1}{1\cdot 2\cdot 3} + \frac{1}{2\cdot 3\cdot 4} + \ldots + \frac{1}{n(n+1)(n+2)}$ Can someone help me with this problem?
Finding the limit $\lim_{n \to \infty}\ x_n$ where
$$x_n = \frac{1}{1\cdot 2\cdot 3} + \frac{1}{2\cdot 3\cdot 4} + \ldots + \frac{1}{n(n+1)(n+2)},\quad n\in\mathbb{N}.$$
I don't have a clue how to do this.

Use $$\frac{1}{n(n+1)(n+2)}=\frac{1}{2n(n+1)}-\frac{1}{2(n+1)(n+2)}.$$
