1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=?

来源：学生作业帮助网编辑：作业帮时间：2024/05/05 06:23:25

1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=?
1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=?

1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=?
1×1/2=1/2=1-1/2
1/2×1/3=1/6=1/2-1/3
1/3×1/4=1/12=1/3-1/4
.
1/2005×1/2006=1/2005-1/2006
所以1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006
=1-1/2+1/2-1/3+1/3-1/4+.+1/2005-1/2006
=1-1/2006
=2005/2006

原式=1-1/2+1/2-1/3+1/3-1/4……+1/2005-1/2006
=1-1/2006
=2005/2006

1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006
=(1-1/2)+(1/2-1/3)+(1/3-1/4)……+(1/2005-1/2006)
=1-1/2006
=2005/2006