(1/2+1/3+1/4+1/5+1/6+.+1/2013)*(1+1/2+..+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+.+1/2012)(1/2+1/3+1/4+1/5+1/6+...+1/2013)*(1+1/2+1/3+1/4...+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+1/3+1/4+...+1/2012)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/10 18:39:00
![(1/2+1/3+1/4+1/5+1/6+.+1/2013)*(1+1/2+..+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+.+1/2012)(1/2+1/3+1/4+1/5+1/6+...+1/2013)*(1+1/2+1/3+1/4...+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+1/3+1/4+...+1/2012)](/uploads/image/z/1997027-35-7.jpg?t=%EF%BC%881%2F2%2B1%2F3%2B1%2F4%2B1%2F5%2B1%2F6%2B.%2B1%2F2013%EF%BC%89%2A%EF%BC%881%2B1%2F2%2B..%2B1%2F2012%EF%BC%89-%EF%BC%881%2B1%2F2%2B1%2F3%2B1%2F4%2B...%2B1%2F2013%EF%BC%89%2A%EF%BC%881%2F2%2B.%2B1%2F2012%EF%BC%89%EF%BC%881%2F2%2B1%2F3%2B1%2F4%2B1%2F5%2B1%2F6%2B...%2B1%2F2013%EF%BC%89%2A%EF%BC%881%2B1%2F2%2B1%2F3%2B1%2F4...%2B1%2F2012%EF%BC%89-%EF%BC%881%2B1%2F2%2B1%2F3%2B1%2F4%2B...%2B1%2F2013%EF%BC%89%2A%EF%BC%881%2F2%2B1%2F3%2B1%2F4%2B...%2B1%2F2012%EF%BC%89)
(1/2+1/3+1/4+1/5+1/6+.+1/2013)*(1+1/2+..+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+.+1/2012)(1/2+1/3+1/4+1/5+1/6+...+1/2013)*(1+1/2+1/3+1/4...+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+1/3+1/4+...+1/2012)
(1/2+1/3+1/4+1/5+1/6+.+1/2013)*(1+1/2+..+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+.+1/2012)
(1/2+1/3+1/4+1/5+1/6+...+1/2013)*(1+1/2+1/3+1/4...+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+1/3+1/4+...+1/2012)
(1/2+1/3+1/4+1/5+1/6+.+1/2013)*(1+1/2+..+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+.+1/2012)(1/2+1/3+1/4+1/5+1/6+...+1/2013)*(1+1/2+1/3+1/4...+1/2012)-(1+1/2+1/3+1/4+...+1/2013)*(1/2+1/3+1/4+...+1/2012)
设1/2+1/3+1/4+...+1/2012=A
那么上述式
=(A+1/2013)*(A+1)-(1+A+1/2013)*A
分解后
=A²+(1+1/2013)A+1/2013-A²-(1+1/2013)A
=1/2013
你不知道提供应室,自己算
=a*b-(1+a)(b-1)=a*b-(b-1+a*b-a)=a-b+1=(1/2+1/3+1/4+1/5+1/6+...+1/2013)-(1+1/2+1/3+1/4...+1/2012)+1=1/2013