化简:|1/2-1|+|1/3-1/2|+|1/4-1/3|+……+|1/2010-1/2009|

问题描述:

化简:|1/2-1|+|1/3-1/2|+|1/4-1/3|+……+|1/2010-1/2009|

原式=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010