(-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](/uploads/image/z/7130922-42-2.jpg?t=%28-1x1%2F2%29%2B%28-1%2F2x1%2F3%29%2B.%2B%28-1%2F2011x1%2F2011%29%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91)
(-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