计算1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(19×21)

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计算1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(19×21)

计算1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(19×21)
计算1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(19×21)

计算1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.+1/(19×21)
原式=1/2(1/1-1/3+1/3-1/5+1/5-1/7+.+1/19-1/21)
=1/2*20/21
=20/42
=10/21

=0.5*(1/1-1/3+1/3-1/5+。。。+1/19-1/21)
=0.5*(1-1/21)
=10/21

10/21 用裂项公式

1/(1x3)+1/(3x5)+1/(5x7)+......+1/(19x21)=1/2x(1-1/3+1/3-1/5+1/5-1/7+.......+1/19-1/21)
=1/2x(1-1/21)=10/21