1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+···+1/(x+2012)(y+2012)
=1/1x2+1/2x3+1/3x4+...+1/2013x2014
=1-1/2+1/2+1/3+1/3-1/4+...+1/2013-1/2014
=1-1/2014
=2013/2014
若x=1 y=2 求：1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+···+1/(x+2012)(y+2
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