(1/2+1/3+...+1/2007)*(1+1/2+1/3+...+1/2006)-(1+1/2+1/3+...+/2007)*(1/2+1/3+...+1/2006)
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![(1/2+1/3+...+1/2007)*(1+1/2+1/3+...+1/2006)-(1+1/2+1/3+...+/2007)*(1/2+1/3+...+1/2006)](/uploads/image/z/2717135-71-5.jpg?t=%EF%BC%881%2F2%2B1%2F3%2B...%2B1%2F2007%29%2A%281%2B1%2F2%2B1%2F3%2B...%2B1%2F2006%EF%BC%89-%EF%BC%881%2B1%2F2%2B1%2F3%2B...%2B%2F2007%29%2A%EF%BC%881%2F2%2B1%2F3%2B...%2B1%2F2006%EF%BC%89)
(1/2+1/3+...+1/2007)*(1+1/2+1/3+...+1/2006)-(1+1/2+1/3+...+/2007)*(1/2+1/3+...+1/2006)
(1/2+1/3+...+1/2007)*(1+1/2+1/3+...+1/2006)-(1+1/2+1/3+...+/2007)*(1/2+1/3+...+1/2006)
(1/2+1/3+...+1/2007)*(1+1/2+1/3+...+1/2006)-(1+1/2+1/3+...+/2007)*(1/2+1/3+...+1/2006)
设a=1/2+1/3+...+1/2007,b=1/2+1/3+...+1/2006
则原式=a(b+1)-(a+1)b
=ab+a-ab-b
=a-b
=1/2007