Question

初一解方程

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

Answer 1

1/2(y+1)+1/3(y+2)+1/4(y+3)+…+1/2007(y+2006)=2006
两边同时加上1/2+1/3+1/4+...+1/2007
1/2(y+1)+1/2+1/3(y+2)+1/3+…+1/2007(y+2006)+1/2007
=2006+1/2+1/4+...+1/2007

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

Answer 2

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