计算:(1/2+1/3+1/4+…+1//2006)(1+1/2+1/3+…+1/2005)-(1+1/2+1/3+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:2024/07/31 06:36:17
计算:(1/2+1/3+1/4+…+1//2006)(1+1/2+1/3+…+1/2005)-(1+1/2+1/3+1/4+…+1/2006)(1/2+1/3+…+1/2005)
![计算:(1/2+1/3+1/4+…+1//2006)(1+1/2+1/3+…+1/2005)-(1+1/2+1/3+1/](/uploads/image/z/4517438-14-8.jpg?t=%E8%AE%A1%E7%AE%97%EF%BC%9A%EF%BC%881%2F2%2B1%2F3%2B1%2F4%2B%E2%80%A6%2B1%2F%2F2006%EF%BC%89%EF%BC%881%2B1%2F2%2B1%2F3%2B%E2%80%A6%2B1%2F2005%EF%BC%89-%EF%BC%881%2B1%2F2%2B1%2F3%2B1%2F)
(1/2+1/3+1/4+…+1/2006)(1+1/2+1/3+…+1/2005)-(1+1/2+1/3+…+1/2006)(1/2+1/3+…1/2005)
=(1+1/2+1/3+1/4+…+1/2006)(1+1/2+1/3+…+1/2005)-(1+1/2+1/3+…+1/2005)-(1+1/2+1/3+…+1/2006)(1/2+1/3+…1/2005)
=(1+1/2+1/3+1/4+…+1/2006)*1-(1+1/2+1/3+…+1/2005)
=1/2006
就这样答案为1/2006
=(1+1/2+1/3+1/4+…+1/2006)(1+1/2+1/3+…+1/2005)-(1+1/2+1/3+…+1/2005)-(1+1/2+1/3+…+1/2006)(1/2+1/3+…1/2005)
=(1+1/2+1/3+1/4+…+1/2006)*1-(1+1/2+1/3+…+1/2005)
=1/2006
就这样答案为1/2006