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第16页

信息发布者：

$=1−( \frac {1}{4}−\frac {1}{5})−(\frac {1}{5}−\frac {1}{6})−(\frac {1}{6}−\frac {1}{7})−(\frac {1}{7}−\frac {1}{8})$

$−(\frac {1}{8}−\frac {1}{9})−(\frac {1}{9}−\frac {1}{10})$

$=1−\frac {1}{4}+\frac {1}{5}-\frac {1}{5}+\frac {1}{6}−\frac {1}{6}+\frac {1}{7}−\frac {1}{7}+\frac {1}{8}−\frac {1}{8}$

$+\frac {1}{9}-\frac {1}{9}+\frac {1}{10}$

$=1−\frac {1}{4}+\frac {1}{10}$

$=\frac {3}{4}+\frac {1}{10}$

$=\frac {17}{20}$

$=(1−\frac {1}{2})+ (1−\frac {1}{6})+(1−\frac {1}{12})+…...+(1−\frac {1}{380})$

$=19−(\frac {1}{2}+\frac {1}{6}+\frac {1}{12}+.…+\frac {1}{380})$

$=19−(\frac {1}{1×2}+\frac {1}{2×3}+\frac {1}{3×4}+.….+\frac {1}{19×20})$

$=19−(1−\frac {1}{2}+\frac {1}{2}-\frac {1}{3}+\frac {1}{3}-\frac {1}{4}+...+\frac {1}{19}−\frac {1}{20})$

$=19−(1−\frac {1}{20})$

$=19−\frac {19}{20}$

$=18\frac {1}{20}$