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来源:百度文库 编辑:高考问答 时间:2024/05/08 14:36:20
用裂项法原式={2/(1*2)-2/(2*3)+2/(2*3)-2/(3*4)+.......-2/[(n+1)*(n+2)]}*(1/2) ={2/(1*2)-2/[(n+1)*(n+2)]}*(1/2) ={1-2/[(n+1)*(n+2)]}*(1/2) =1/2-1/[(n+1)(n+2)]