第13页 - 亮点给力提优课时作业本六年级数学江苏版

$ =(1-\frac{1}{2})+(1-\frac {1}{6})+(1-\frac {1}{12})+(1-\frac {1}{20})$

$+...+(1-\frac {1}{72})$

$=8-(\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+\frac {1}{20}+...+\frac {1}{72})$

$=8-(1-\frac {1}{2}+\frac {1}{2}-\frac {1}{3}+\frac {1}{3}-\frac {1}{4}+\frac {1}{4}-\frac {1}{5}$

$+...+\frac {1}{8}-\frac {1}{9})$

$=8-\frac {8}{9}$

$=7 \frac {1}{9}$

$ \frac {2}{63}$

$ \frac {1}{63}$

13

$ \frac {2}{143}$

$ \frac {1}{11}$

$ \frac {1}{13}$

$ \frac {1}{143}$

$=1-\frac {1}{2}+\frac {1}{2}-\frac {1}{3}+\frac {1}{3}-\frac {1}{4}+...+\frac {1}{2023}-\frac {1}{2024}$

$=1-\frac {1}{2024}$

$=\frac {2023}{2024}$

$=\frac{1}{2}×(\frac{1}{3}-\frac{1}{5}+\frac {1}{5}-\frac {1}{7}+\frac {1}{7}-\frac {1}{9}+...+\frac {1}{97}-\frac {1}{99})$

$=\frac{1}{2}×\frac {32}{99}$

$=\frac {16}{99}$