(1/2+1/3+...+1/2005)(1+1/2+1/3+...+1/2004)-(1+1/2+1/3+...+1/2005)(1/2+1/3+...+1/2004)
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(1/2+1/3+...+1/2005)(1+1/2+1/3+...+1/2004)-(1+1/2+1/3+...+1/2005)(1/2+1/3+...+1/2004)
(1/2+1/3+...+1/2005)(1+1/2+1/3+...+1/2004)-(1+1/2+1/3+...+1/2005)(1/2+1/3+...+1/2004)
(1/2+1/3+...+1/2005)(1+1/2+1/3+...+1/2004)-(1+1/2+1/3+...+1/2005)(1/2+1/3+...+1/2004)
用奥数中的换元法做
假设A=1/2+1/3+……+1/2005,B=1+1/2+1/3+……+1/2005
原式=A×(B -1/2005)-B×(A -1/2005)
=A×B-A×1/2005-A×B+B×1/2005
=B×1/2005-A×1/2005
=(B-A)×1/2005 B-A=1,B里面比A多一个数,是1
=1×1/2005
=1/2005