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

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)=?
1个回答 分类:综合 2014-10-16

问题解答:

我来补答
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
 
 
展开全文阅读
剩余:2000