1. 巧算：$1\frac{1}{2}+2\frac{1}{4}+3\frac{1}{8}+4\frac{1}{16}+5\frac{1}{32}+6\frac{1}{64}+7\frac{1}{128}$

$1\frac{1}{2}+2\frac{1}{4}+\dots+7\frac{1}{128}=(1+2+\dots+7)+(\frac{1}{2}+\frac{1}{4}+\dots+\frac{1}{128})=28+(1-\frac{1}{128})=28\frac{127}{128}$

2. $\frac{1}{2}=1-\frac{1}{2},\frac{1}{6}=\frac{1}{2}-\frac{1}{3},\frac{1}{12}=\frac{1}{3}-\frac{1}{4}……$根据规律计算下面的题目。
$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+……+\frac{1}{90}$

$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\dots+\frac{1}{90}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\dots+\frac{1}{9}-\frac{1}{10}=\frac{9}{10}$

3. $1 - 0.5 - \frac{1}{6} - \frac{1}{12} - 0.05 - \frac{1}{30}$的结果是多少？

$1-0.5-\frac{1}{6}-\frac{1}{12}-0.05-\frac{1}{30}=1-\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}=1-(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30})=1-(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\dots+\frac{1}{5}-\frac{1}{6})=1-(1-\frac{1}{6})=\frac{1}{6}$