作业帮数学(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)=?
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 18:30:30
数学(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)=?
数学(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)=?
数学(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)=?
(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/2007-1/2008)
=1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008
=1+（-1/2+1/2）+（-1/3+1/3）+（-1/4+1/4）...+（-1/2007+1/2007）-1/2008
=1-1/2008
=2007/2008
去括号，消项就可以了！
括号展开就一目了然了
=1-1/2+1/2-1/3+1/3-1/4+...+1/2007-1/2008
=1+（-1/2+1/2）+（-1/3+1/3）+（-1/4+1/4）...+（-1/2007+1/2007）-1/2008
=1-1/2008
=2007/2008