(2000-1999-1980-1970+…+20-10)/(1-1/2)(1-1/3)(1-1/4)…(1-1/998)(1-1/999)(1-1/1000)

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(2000-1999-1980-1970+…+20-10)/(1-1/2)(1-1/3)(1-1/4)…(1-1/998)(1-1/999)(1-1/1000)
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(2000-1999-1980-1970+…+20-10)/(1-1/2)(1-1/3)(1-1/4)…(1-1/998)(1-1/999)(1-1/1000)
(2000-1999-1980-1970+…+20-10)/(1-1/2)(1-1/3)(1-1/4)…(1-1/998)(1-1/999)(1-1/1000)

(2000-1999-1980-1970+…+20-10)/(1-1/2)(1-1/3)(1-1/4)…(1-1/998)(1-1/999)(1-1/1000)
(1-1/2)(1-1/3)(1-1/4)…(1-1/998)(1-1/999)(1-1/1000)
=(1/2)*(2/3)*(3/4)*...*(999/1000)=1/1000
(2000-1990)+(1980-1970)+…+(20-10)=10*100=1000
2000-1990+1980-1970+…+20-10除以(1-1/2)(1-1/3)(1-1/4)…(1-1/998)(1-1/999)(1-1/1000)=1000/(1/1000)=100000