1计算(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/07/30 22:07:02
1计算
(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17+1/19)(1/11+1/13+1/17)
2计算
(1/2+1/3+.+1/2005)(1+1/2+1/3+.+1/2004)-(1+1/2+...+1/2005)(1/2+1/3+...+1/2004)
(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17+1/19)(1/11+1/13+1/17)
2计算
(1/2+1/3+.+1/2005)(1+1/2+1/3+.+1/2004)-(1+1/2+...+1/2005)(1/2+1/3+...+1/2004)
![1计算(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17](/uploads/image/z/1392016-40-6.jpg?t=1%E8%AE%A1%E7%AE%97%EF%BC%881%2B1%EF%BC%8F11%2B1%EF%BC%8F13%2B1%EF%BC%8F17%EF%BC%89%EF%BC%881%EF%BC%8F11%2B1%EF%BC%8F13%2B1%EF%BC%8F17%2B1%EF%BC%8F19%EF%BC%89-%EF%BC%881%2B1%EF%BC%8F11%2B1%EF%BC%8F13%2B1%EF%BC%8F17)
第一题:
先把减号后面这一式子拆开:
(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17+1/19)(1/11+1/13+1/17)
=(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17)(1/11+1/13+1/17)-1/19(1/11+1/13+1/17)
=(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19-1/11-1/13-1/17)-1/19(1/11+1/13+1/17)
=1/19(1+1/11+1/13+1/17)-1/19(1/11+1/13+1/17)
=1/19(1+1/11+1/13+1/17-1/11-1/13-1/17)
=1/19
第二题:
与前一题的解法一样,先把减号后面这一式子拆开:
(1/2+1/3+.+1/2005)(1+1/2+1/3+.+1/2004)-(1+1/2+...+1/2005)(1/2+1/3+...+1/2004)
=(1/2+1/3+.+1/2005)(1+1/2+1/3+.+1/2004)-(1/2+1/3+...+1/2005)(1/2+1/3+...+1/2004)-(1/2+1/3+...+1/2004)
=(1/2+1/3+.+1/2005)(1+1/2+1/3+.+1/2004 -1/2-1/3-...-1/2004)-(1/2+1/3+...+1/2004)
=(1/2+1/3+.+1/2004+1/2005)-(1/2+1/3+...+1/2004)
= 1/2005
先把减号后面这一式子拆开:
(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17+1/19)(1/11+1/13+1/17)
=(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19)-(1+1/11+1/13+1/17)(1/11+1/13+1/17)-1/19(1/11+1/13+1/17)
=(1+1/11+1/13+1/17)(1/11+1/13+1/17+1/19-1/11-1/13-1/17)-1/19(1/11+1/13+1/17)
=1/19(1+1/11+1/13+1/17)-1/19(1/11+1/13+1/17)
=1/19(1+1/11+1/13+1/17-1/11-1/13-1/17)
=1/19
第二题:
与前一题的解法一样,先把减号后面这一式子拆开:
(1/2+1/3+.+1/2005)(1+1/2+1/3+.+1/2004)-(1+1/2+...+1/2005)(1/2+1/3+...+1/2004)
=(1/2+1/3+.+1/2005)(1+1/2+1/3+.+1/2004)-(1/2+1/3+...+1/2005)(1/2+1/3+...+1/2004)-(1/2+1/3+...+1/2004)
=(1/2+1/3+.+1/2005)(1+1/2+1/3+.+1/2004 -1/2-1/3-...-1/2004)-(1/2+1/3+...+1/2004)
=(1/2+1/3+.+1/2004+1/2005)-(1/2+1/3+...+1/2004)
= 1/2005