(-1x1/2)+(-1/2x1/3)+.+(-1/2011x1/2011)等于多少
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(-1x1/2)+(-1/2x1/3)+.+(-1/2011x1/2011)等于多少(-1x1/2)+(-1/2x1/3)+.+(-1/2011x1/2011)等于多少(-1x1/2)+(-1/2x1
(-1x1/2)+(-1/2x1/3)+.+(-1/2011x1/2011)等于多少
(-1x1/2)+(-1/2x1/3)+.+(-1/2011x1/2011)等于多少
(-1x1/2)+(-1/2x1/3)+.+(-1/2011x1/2011)等于多少
(-1x1/2)+(-1/2x1/3)+.+(-1/2010x1/2011)
=-1+1/2-1/2+1/3-1/3+1/4-……-1/2010+1/2011
=-1+1/2011
=-2010/2011
=-1+1/2-1/2+1/3+。。。-1/2010+1/2011=-2010/2011
原式=-(1/1×2+1/2×3+……+1/2010×2011）
=-（1-1/2+1/2-1/3+……+1/2010-1/2011）
=-（1-1/2011）
=-2010/2011
裂项法
1/（2×3）=1/2-1/3