2. 运用规律计算下面各题。
(1)$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\frac{1}{128}$
(2)$\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\dots+\frac{1}{512}$

2.(1) $\frac{127}{128}$ (2) $\frac{511}{512}$

思路点拨一个分数的分母如果是两个相邻非零自然数的乘积，分子是1，即看作$\frac{1}{n×(n+1)}$，可以转化成$(\frac{1}{n}-\frac{1}{n+1})$。即$\frac{1}{30}$看作$\frac{1}{5×6}$，可以转化成$(\frac{1}{5}-\frac{1}{6})$，$\frac{1}{42}$看作$\frac{1}{6×7}$，可以转化成$(\frac{1}{6}-\frac{1}{7})$，$\frac{1}{56}$看作$\frac{1}{7×8}$，可以转化成$(\frac{1}{7}-\frac{1}{8})$。
答案详解 $\frac{1}{5}-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}$
$=\frac{1}{5}-(\frac{1}{5}-\frac{1}{6})-(\frac{1}{6}-\frac{1}{7})-(\frac{1}{7}-\frac{1}{8})$
$=\frac{1}{5}-\frac{1}{5}+\frac{1}{6}-\frac{1}{6}+\frac{1}{7}-\frac{1}{7}+\frac{1}{8}$
$=\frac{1}{8}$

$\frac{1}{5}-\frac{1}{30}-\frac{1}{42}-\frac{1}{56}$
$=\frac{1}{5}-(\frac{1}{5}-\frac{1}{6})-(\frac{1}{6}-\frac{1}{7})-(\frac{1}{7}-\frac{1}{8})$
$=\frac{1}{5}-\frac{1}{5}+\frac{1}{6}-\frac{1}{6}+\frac{1}{7}-\frac{1}{7}+\frac{1}{8}$
$=\frac{1}{8}$

3. 运用规律计算下面各题。
(1) $\frac{1}{4} - \frac{1}{20} - \frac{1}{30} - \frac{1}{42} - \frac{1}{56}$
(2) $\frac{1}{3} - \frac{1}{12} - \frac{1}{20} - \frac{1}{30} - \frac{1}{42} - \frac{1}{56}$

3.(1) $\frac{1}{8}$ (2) $\frac{1}{8}$