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python/数学课程/有理数巧算之裂项相消.md

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答:\large \frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2018}-\frac{1}{2019}=\frac{2018}{2019}

\because \large \frac{3}{4 \times 7}=\frac{1}{4}-\frac{1}{7}

\therefore \large 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{46}-\frac{1}{56}=\frac{55}{56}

总结: