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

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

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
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

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
|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