七年级数学题若X-1的绝对值+(XY-2)平方=0,求1/XY+1/(X+1)(Y+1)+1/(X+2)(Y+2)+----+1/(X+2011)(Y+2011)的值

问题描述:

七年级数学题若X-1的绝对值+(XY-2)平方=0,求1/XY+1/(X+1)(Y+1)+1/(X+2)(Y+2)+----+1/(X+2011)(Y+2011)的值

因为绝对值和平方的结果都不小于0,因此只有两部分都为0时才成立
X-1=0,X=1
XY-2=0,XY=2,Y=2
1/(1×2)=1/1-1/2,1/(2×3)=1/2-1/3,1/(3×4)=1/3-1/4...
所以
原式=1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2012×2013)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2012-1/2013
=1-1/2013
=2012/2013