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原式= 1 + 1/(2*3)+ 1 +1/(3*4)+ 1 +1/(4*5)+ .+ 1 +1/(20*21) =19 +(1/2 -1/3)+(1/3 -1/4)+(1/4 -1/5)+ .+(1/20 -1/21) = 19 + 1/2 -1/21 =19又19/42
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