用简便方法计算|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2011-1/2010|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|+...+|1/2011-1/2010|的值
用简便方法计算|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2011-1/2010|的值

用简便方法计算|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2011-1/2010|的值
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2011-1/2010|
=|1/2-1/3|+|1/3-1/4|+|1/4-1/5|+...+|1/2010-1/2011|
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/2010-1/2011
= 1/2 - 1/2011
=(2011-2)/4022
=2009/4022