数学题(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/5+1/6+...+1/670）=?|高中数学问答-字典翻译问答网

字典翻译问答高中数学数学题(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/5+1/6+...+1/670）=?

问题标题：

数学题(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/5+1/6+...+1/670）=?

问题描述：

数学题(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/

(1/4+1/5+1/6+...+1/671)(1/3+1/4+1/5+..+1/670)-(1/3+1/4+1/5+...+1/671)(1/4+1/5+1/6+...+1/670）=?

陈夏光回答：

　　用换元法做,假设A=1/4+1/5+……+1/670,B=1/3+1/4+1/5+……+1/670 　　原式=(A+1/671)×B-(B+1/671)×A 　　=A×B+1/671×B-A×B-1/671×A 　　=1/671×B-1/671×A 　　=1/671×(B-A)（B-A=1/3,B比一个分数1/3）　　=1/671×1/3 　　=1/2013

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