已知|xy-2|与|y-2|互为相反数,试求代数式1/xy+1/(x+1)*(y+1)+1/(x+2)*(y+2)+.+1/(x+2014)*(y+2014)的值.

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已知|xy-2|与|y-2|互为相反数,试求代数式1/xy+1/(x+1)*(y+1)+1/(x+2)*(y+2)+.+1/(x+2014)*(y+2014)的值.

已知|xy-2|与|y-2|互为相反数,试求代数式1/xy+1/(x+1)*(y+1)+1/(x+2)*(y+2)+.+1/(x+2014)*(y+2014)的值.
已知|xy-2|与|y-2|互为相反数,试求代数式1/xy+1/(x+1)*(y+1)+1/(x+2)*(y+2)+.+1/(x+2014)*(y+2014)的值.

已知|xy-2|与|y-2|互为相反数,试求代数式1/xy+1/(x+1)*(y+1)+1/(x+2)*(y+2)+.+1/(x+2014)*(y+2014)的值.
∵|xy-2|与|y-2|互为相反数
∴|xy-2|+|y-2|=0
∴xy-2=0
y-2=0
∴x=1
y=2
∴1/xy+1/(x+1)*(y+1)+1/(x+2)*(y+2)+.+1/(x+2014)*(y+2014)
=1/1×2+1/2×3+1/3×4+……+1/2015×2016
=1-1/2+1/2-1/3+1/3-1/4+……+1/2015-1/2016
=1-1/2016
=2015/2016