简便计算,(1-1/2+1/3-1/4+1/5-…+1/2007-1/2008)/(1/1005+1/1006+1/10
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:2024/06/23 22:19:10
简便计算,
(1-1/2+1/3-1/4+1/5-…+1/2007-1/2008)/(1/1005+1/1006+1/1007+…1/2007+1/2008)
(1-1/2+1/3-1/4+1/5-…+1/2007-1/2008)/(1/1005+1/1006+1/1007+…1/2007+1/2008)
![简便计算,(1-1/2+1/3-1/4+1/5-…+1/2007-1/2008)/(1/1005+1/1006+1/10](/uploads/image/z/797703-15-3.jpg?t=%E7%AE%80%E4%BE%BF%E8%AE%A1%E7%AE%97%2C%281-1%2F2%2B1%2F3-1%2F4%2B1%2F5-%E2%80%A6%2B1%2F2007-1%2F2008%29%2F%281%2F1005%2B1%2F1006%2B1%2F10)
(1-1/2+1/3-1/4+1/5-…+1/2007-1/2008)/(1/1005+1/1006+1/1007+…1/2007+1/2008)
=[1-(1-1/2)+(1/2-1/3)+(1/3-1/4)……+(1/2007-1/2008)]/[1/1005+(1/1005-1/1006)+(1/1006-1/1007)+……+(1/2007-1/2008)]
=(1/2008)/(1/2008)=1
又让我回想起了高中时代啊,
=[1-(1-1/2)+(1/2-1/3)+(1/3-1/4)……+(1/2007-1/2008)]/[1/1005+(1/1005-1/1006)+(1/1006-1/1007)+……+(1/2007-1/2008)]
=(1/2008)/(1/2008)=1
又让我回想起了高中时代啊,