帮个忙巧算:(3/1*2)-(3/2*3)-(3/3*4) -…-(3/2007*2008)

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帮个忙巧算:(3/1*2)-(3/2*3)-(3/3*4) -…-(3/2007*2008)

帮个忙巧算:(3/1*2)-(3/2*3)-(3/3*4) -…-(3/2007*2008)
帮个忙
巧算:(3/1*2)-(3/2*3)-(3/3*4) -…-(3/2007*2008)

帮个忙巧算:(3/1*2)-(3/2*3)-(3/3*4) -…-(3/2007*2008)
(3/1*2)-(3/2*3)-(3/3*4) -…-(3/2007*2008)
=3*(1/1*2-1/2*3-1/3*4-...-1/2007*2008)
=3*[(1-1/2)-(1/2-1/3)-(1/3-1/4)-...-(1/2007-1/2008)]
=3*[1-1/2-1/2+1/3-1/3+1/4-...-1/2007+1/2008]
=3*1/2008
=3/2008

原式=3*(2/1-3/2-4/3-5/4-6/5-…-2008/2007)
后面用计算器算

(3/1*2)-(3/2*3)-(3/3*4) -…-(3/2007*2008)
=-3(1/2-1+1/2-1/3+1/3-1/4+...+1/2007-1/2008)
=-3×(-1/2008)
=3/2008

很简单啊,把3提出来,1/1*2=1/1 - 1/2 1/2*3=1/2 - 1/3 以此类推 中间的都相互减掉了 最后就是3*(1-1/2008)=6021/2008