1/2 + 1/6 + ... + 1/(n^2 + n) = ?

$1/2 + 1/6\\ =2/3$

$1/2 + 1/6 + 1/12\\ =2/3 + 1/12\\ =3/4$

$\therefore 1/2 + 1/6 +...+\dfrac{1}{n^2+n} = \dfrac{n}{n+1}$