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:2024/06/16 18:47:48
![1×1/2+1/2×1/3+1/3×1/4……+1/2005×1/2006=?](/uploads/image/z/1682027-35-7.jpg?t=1%C3%971%2F2%2B1%2F2%C3%971%2F3%2B1%2F3%C3%971%2F4%E2%80%A6%E2%80%A6%2B1%2F2005%C3%971%2F2006%3D%3F)
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