已知x=1/3,y=-1/2,求代数式x-(x+y)+(x+2y)-(x+3y)+(x+4y)-(x+5y)+...-(x+2009y)的值.

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已知x=1/3,y=-1/2,求代数式x-(x+y)+(x+2y)-(x+3y)+(x+4y)-(x+5y)+...-(x+2009y)的值.已知x=1/3,y=-1/2,求代数式x-(x+y)+(x

已知x=1/3,y=-1/2,求代数式x-(x+y)+(x+2y)-(x+3y)+(x+4y)-(x+5y)+...-(x+2009y)的值.
已知x=1/3,y=-1/2,求代数式x-(x+y)+(x+2y)-(x+3y)+(x+4y)-(x+5y)+...-(x+2009y)的值.

已知x=1/3,y=-1/2,求代数式x-(x+y)+(x+2y)-(x+3y)+(x+4y)-(x+5y)+...-(x+2009y)的值.
x全部抵消了,提出y得,原式=y(-1+2-3+4-5+...+2008-2009)=-1/2*(1004-2009)=1005/2


x-(x+y)+(x+2y)-(x+3y)+(x+4y)-(x+5y)+...-(x+2009y)
=-y-y-……-y(共1005个)
=-1005y=-1005*(-1/2)=1005/2

原式=x-x+x-x+……-x+(2-1+4-3+5-4+……+2008-2007-2009)y
=0+(1×1004-2009)y
=-1005y
=1005/2