(1/2+1/3+...+1/2006)(1+1/2+...+1/2005)-(1+1/2+...1/2006)(1/2+1/3+...1/2005)

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 15:36:39
(1/2+1/3+...+1/2006)(1+1/2+...+1/2005)-(1+1/2+...1/2006)(1/2+1/3+...1/2005)
x){PHPX[OOHijXSM]\ BTMR>M/+_2TXStV

(1/2+1/3+...+1/2006)(1+1/2+...+1/2005)-(1+1/2+...1/2006)(1/2+1/3+...1/2005)
(1/2+1/3+...+1/2006)(1+1/2+...+1/2005)-(1+1/2+...1/2006)(1/2+1/3+...1/2005)

(1/2+1/3+...+1/2006)(1+1/2+...+1/2005)-(1+1/2+...1/2006)(1/2+1/3+...1/2005)
设(1+1/2+1/3+...+1/2005+1/2006)=x,则原式=(x-1)(x-1/2006)-x(x-1-1/2006) =x²-1/2006x-x+1/2006-x²+x+1/2006x =1/2006