1/2(x+1)+1/3(x+2)+1/4(x+3)+.+1/2007(x+2006)=2006

題目：

1/2(x+1)+1/3(x+2)+1/4(x+3)+.+1/2007(x+2006)=2006

解答：

1/2x+1/2+1/3x+2/3+1/4x+3/4+……+1/2007x+2006/2007=1+1+1+……+1
(1/2+1/3+……+1/2007)x=(1-1/2)+(1-2/3)+……+(1-2006/2007)
(1/2+1/3+……+1/2007)x=1/2+1/3+……+1/2007
x=1