(-1×1/2)+(-1/2×1/3)+(1/3×1/4)+…+(-1/2011×1/2012)+(-1/2012×1/2013)=?
题目
(-1×1/2)+(-1/2×1/3)+(1/3×1/4)+…+(-1/2011×1/2012)+(-1/2012×1/2013)=?
答案
(-1×1/2)+(-1/2×1/3)+(1/3×1/4)+…+(-1/2011×1/2012)+(-1/2012×1/2013)
=(1/2-1)+(1/3-1/2)+(1/4-1/3)+(1/5-1/4)+(1/6-1/5)+.+(1/2013-1/2012)
=-1+1/2+1/3-1/2+1/4-1/3+1/5-1/4+1/6-1/5+.1/2013-1/2012(消除正负对应的数)
=-1+1/2013
=-2012/2013
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