计算:1×3分之1+2×4分之1+3×5分之1……+18×20分之1
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1/1×3+1/2×4+1/3×5……+1/18×20
=(1-1/3)/2+(1/2-1/4)/2+(1/3-1/5)/2+(1/4-1/6)/2+.+(1/17-1/19)/2+(1/18-1/20)/2
=(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.+1/17-1/19+1/18-1/20)/2
=(1+1/2-1/19-1/20)/2
=(3/2-39/380)/2
=(531/380)/2
=531/760
=(1-1/3)/2+(1/2-1/4)/2+(1/3-1/5)/2+(1/4-1/6)/2+.+(1/17-1/19)/2+(1/18-1/20)/2
=(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.+1/17-1/19+1/18-1/20)/2
=(1+1/2-1/19-1/20)/2
=(3/2-39/380)/2
=(531/380)/2
=531/760
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