《2025年阳光同学暑假衔接五升六年级数学北师大版》

例2 巧算：$\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+\frac {1}{30}$。

答案： $\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+\frac {1}{30}$
$=(1-\frac {1}{2})+(\frac {1}{2}-\frac {1}{3})+(\frac {1}{3}-\frac {1}{4})+$
$(\frac {1}{4}-\frac {1}{5})+(\frac {1}{5}-\frac {1}{6})$
$=1-\frac {1}{6}$
$=\frac {5}{6}$

2. (仿例练习)巧算：$\frac {1}{2×3}+\frac {1}{3×4}+\frac {1}{4×5}+\frac {1}{5×6}+\frac {1}{6×7}$。

答案： $\frac {5}{14}$

3. (变式提升)计算。
$\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+\frac {1}{30}+\frac {1}{42}$            $\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+\frac {1}{30}+... +\frac {1}{90}$

答案： $\frac {6}{7}$ $\frac {9}{10}$