7. 观察下列式子的特征：
$\frac{1}{2} = \frac{1}{1 × 2} = 1 - \frac{1}{2}$
$\frac{1}{6} = \frac{1}{2 × 3} = \frac{1}{2} - \frac{1}{3}$
$\frac{1}{12} = \frac{1}{3 × 4} = \frac{1}{3} - \frac{1}{4}$
$\frac{1}{20} = \frac{1}{4 × 5} = \frac{1}{4} - \frac{1}{5}$
根据前面等式的特征及其计算规律，用简便方法计算下题。
$\frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20}$

$\begin{aligned}&\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}\\=&(1-\frac{1}{2})+(\frac{1}{2}-\frac{1}{3})+(\frac{1}{3}-\frac{1}{4})+(\frac{1}{4}-\frac{1}{5})\\=&1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\\=&1-\frac{1}{5}\\=&\frac{4}{5}\end{aligned}$
答：计算结果是$\frac{4}{5}$。