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第14页

信息发布者：

 $1-\dfrac{1}{2}-\dfrac{1}{4}-\dfrac{1}{8}-\dfrac{1}{16}-\dfrac{1}{32}-\dfrac{1}{64}$

 $=1-(\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{16}+\dfrac{1}{32}+\dfrac{1}{64})$

 $=1-(1-\dfrac{1}{64})$

 $=1-\dfrac{63}{64}$

 $=\dfrac{1}{64}$

 $\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{2}{3}+\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4}+\dots+\dfrac{11}{12}$

 $=\dfrac{1}{2}+(\dfrac{1}{3}+\dfrac{2}{3})+(\dfrac{1}{4}+\dfrac{2}{4}+\dfrac{3}{4})+\dots+(\dfrac{1}{12}+\dfrac{2}{12}+\dots+\dfrac{11}{12})$

 $=\dfrac{1}{2}+\dfrac{2}{2}+\dfrac{3}{2}+\dfrac{4}{2}+\dots+\dfrac{11}{2}$

 $=\dfrac{1}{2}+1+\dfrac{3}{2}+2+\dots+\dfrac{11}{2}$

 $=15+\dfrac{36}{2}$

 $=15+18$

 $=33$

$\dfrac{13}{60}$