(2\1+3\1+…+1997\1)*(1+2\1+3\1+…+1996\1)-(1+2\1+3\1+…+1997\1)

学习时间:2026-08-10 18:47:13 阅读：8876

(2\1+3\1+…+1997\1)*(1+2\1+3\1+…+1996\1)-(1+2\1+3\1+…+1997\1)*(2\1+3\1+…+1996\1)

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2026-08-10 18:47:13

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设1/2+1/3+1/4+。。。+1/1997=a,1/2+1/3+。。。+1/1996=b,则原式=a(1+b)-(1+a)b=a+ab-b-ab =a-b=1/2+1/3+1/4+。。。+1/1997-(1/2+1/3+。。。+1/1996) =1/1997