计算:|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2010-1/2009|怎么解

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计算:|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2010-1/2009|怎么解计算:|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2010-

计算:|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2010-1/2009|怎么解
计算:|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2010-1/2009|怎么解

计算:|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2010-1/2009|怎么解
首先把括号去掉:1/3-1/2+1/4-1/3+1/5-1/4+...+1/2010-1/2009 然后你就可以看出第一个数字和第四个数字相减为零,依次这样同数字相减后就只剩下-1/2+1/2010了 所以结果就是 -2008/4020

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2010-1/2009| =1/2-1/3+1/3-1/4+1/4-1/5+...+1/2009-1/2010 =1/2-1/2010 =1005/2010-1/2010 =1004/2010 =502/1005