已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007)=?

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已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007)=?

已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007)=?
已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007)=?

已知x=1,y=2,1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2007)(y+2007)=?
原式=1/1-1/2+1/2-1/3+……+1/2008-1/2009
=1-1/2009
=2008/2009

因为:1/(2*1)=1/1-1/2 1/(2*3)=1/2-1/3 ……
1/n*(n-1)=1/(n-1)-1/n
所以有;1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.....+1/(x+2007)(y+2007)=
=1/1-1/2+1/2-1/3+……+1/2008-1/2009
=1-1/2009
=2008/2009