化简|1/2004-1/2003|+|1/2003-1/2002|+|1/2002-1/2001|+|1/2001-1/2004|=?|1/2004-1/2003|是2004分之1与2003分之1的差的绝对值
来源:学生作业帮助网 编辑:作业帮 时间:2024/11/05 23:22:36
化简|1/2004-1/2003|+|1/2003-1/2002|+|1/2002-1/2001|+|1/2001-1/2004|=?|1/2004-1/2003|是2004分之1与2003分之1的差的绝对值
化简|1/2004-1/2003|+|1/2003-1/2002|+|1/2002-1/2001|+|1/2001-1/2004|=?
|1/2004-1/2003|是2004分之1与2003分之1的差的绝对值
化简|1/2004-1/2003|+|1/2003-1/2002|+|1/2002-1/2001|+|1/2001-1/2004|=?|1/2004-1/2003|是2004分之1与2003分之1的差的绝对值
因为2004分之1与2003分之1的差小于0
所以原式=-1/2004+1/2003-1/2003+1/2002-1/2002+1/2001-1/2001+1/2004 =0
因为2004分之1与2003分之1的差小于0,所以化去绝对值取它的相反数,-(1/2004-1/2003)=-1/2004+1/2003.依次类推.
然后就都被抵消了,最后等于零.
打开绝对值
=1/2003-1/2004+1/2002-1/2003+1/2001-1/2002+1/2001-1/2004
=2/2001
2/2001
|1/2004-1/2003|+|1/2003-1/2002|+|1/2002-1/2001|+|1/2001-1/2004|
=1/2003-1/2004+1/2002-1/2003+1/2001-1/2002+1/2001-1/2004
=2/2001-2/2004
=2(1/2001-1/2004)
=2(3/4010004)
=2/1336668
=1/668334.
原式=1/2003-1/2004+1/2002-1/2003+1/2001- 1/2002+1/2004-1/2001
=0
原式=1/2003-1/2004 + 1/2002-1/2003 +1/2001-1/2002 + 1/2001 - 1/2004
=2/2001 - 2/2004
=6/(2001*2004)