1/1x2+1/2x3+1/3x4+1/4x5+...+1/2008x2009 =？(用简便计算）数学问题请大家帮忙做下

如题所述

1/1x2+1/2x3+1/3x4+1/4x5+...+1/2008x2009 =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/2008-1/2009 =1-1/2009 =2008/2009

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