Question

1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.....+1/(19×21)简便计算怎么做

Answer 1

您好：

1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.....+1/(19×21
=1/2x(1-1/3)+1/2x(1/3-1/5)+...+1/2x(1/19-1/21)
=1/2x(1-1/21)
=10/21

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Answer 2

1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.....+1/(19×21
=1/2x(1-1/3)+1/2x(1/3-1/5)+...+1/2x(1/19-1/21)
=1/2x(1-1/21)
=10/21

Answer 3

原式=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9......+1/19-1/21)
=1/2(1-1/21)
=10/21

Answer 4

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

Answer 5

1/(1×3)+1/(3×5)+1/(5×7)+1/(7×9)+.....+1/(19×21)
=1/2x(1-1/3)+1/2x(1/3-1/5)+...+1/2x(1/19-1/21)
=1/2x(1-1/21)
=10/21