已知x=3分之一,y=-2分之一,求代数式x-(x+y)+(x+2Y)-(x+3y)+(x+4y)...-(x+2009y)

题目

已知x=3分之一,y=-2分之一,求代数式x-(x+y)+(x+2Y)-(x+3y)+(x+4y)...-(x+2009y)

答案

x-(x+y)+(x+2Y)-(x+3y)+(x+4y)...-(x+2009y)
=-y+2y-3y+4y+...-2007y+2008y-2009y
=1004y-2009y
=-1005y
=-1005(-1/2)
=502.5