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）=?

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 16:24:47

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）=?
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）=?

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）=?
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

=（1/3）(1/4+1/5+1/6+...+1/671)-(1/3)(1/4+1/5+1/6+...+1/670)
=(1/3)(1/671)
=1/2013

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