用简便方法计算|1/3-1/2|+|1/4-1/3|+||1/5-1/4|+...+|1/2010-1/2009|的值

分类: 作业答案 • 2021-12-19 15:54:15

问题描述：

答

|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