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原式
= (3+1)/(1×3)-(5+3)/(3×5)+(7+5)/(5×7)-(9+7)/(7×9)+……-(21+19)/(19×21)
= (1+1/3)-(1/3+1/5)+(1/5+1/7)-(1/7+1/9)+……-(1/19+1/21)
= 1+1/3-1/3-1/5+1/5+1/7-1/7-1/9+……-1/19-1/21
= 1-1/21
= 20/21
= (3+1)/(1×3)-(5+3)/(3×5)+(7+5)/(5×7)-(9+7)/(7×9)+……-(21+19)/(19×21)
= (1+1/3)-(1/3+1/5)+(1/5+1/7)-(1/7+1/9)+……-(1/19+1/21)
= 1+1/3-1/3-1/5+1/5+1/7-1/7-1/9+……-1/19-1/21
= 1-1/21
= 20/21
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