谁知道这道题用简便计算怎么算:(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2006*1
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/06/17 04:12:28
谁知道这道题用简便计算怎么算:(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2006*1/2007)只要简便算
![谁知道这道题用简便计算怎么算:(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2006*1](/uploads/image/z/16529861-29-1.jpg?t=%E8%B0%81%E7%9F%A5%E9%81%93%E8%BF%99%E9%81%93%E9%A2%98%E7%94%A8%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%E6%80%8E%E4%B9%88%E7%AE%97%EF%BC%9A%EF%BC%88-1%2A1%2F2%EF%BC%89%2B%EF%BC%88-1%2F2%2A1%2F3%EF%BC%89%2B%EF%BC%88-1%2F3%2A1%2F4%EF%BC%89%2B...%2B%EF%BC%88-1%2F2006%2A1)
(-1*1/2)+(-1/2*1/3)+(-1/3*1/4)+...+(-1/2006*1/2007)
=-[(1*1/2)+(1/2*1/3)+.+(1/2006*1/2007)]
=-[(1/2-1/3)+(1/3-1/4)+.+(1/2006-1/2007)]
=-(1/2-1/3+1/3-1/4+.+1/2006-1/2007)
=-(1/2-1/2007)
=-2005/4014
=-[(1*1/2)+(1/2*1/3)+.+(1/2006*1/2007)]
=-[(1/2-1/3)+(1/3-1/4)+.+(1/2006-1/2007)]
=-(1/2-1/3+1/3-1/4+.+1/2006-1/2007)
=-(1/2-1/2007)
=-2005/4014
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