Prove
$$\sum_{x=0}^\infty \frac{1}{(x+ 1)(x+2)} = 1.$$
I couldn't find this problem solved online and I haven't reviewed series in a long time. I thought maybe squeeze theorem could help? A related question asks to prove
$$ \sum_{x=0}^\infty \frac{x}{(x+ 1)(x+2)} = +\infty.$$