计算1/1×2+1/2×3+1/3×4.1/2011×2012

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计算1/1×2+1/2×3+1/3×4.1/2011×2012
计算1/1×2+1/2×3+1/3×4.1/2011×2012

计算1/1×2+1/2×3+1/3×4.1/2011×2012
注意到:1/2×3=1/2-1/3 ……
1/1×2+1/2×3+1/3×4.+1/2011×2012
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/2011-1/2012) (去括号后,相邻应对数是互为相反数!)
=1-1/2012
=2011/2012

计算
1/1×2+1/2×3+1/3×4......1/2011×2012
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012

1/[n*(n+1)]=1/n-1/(n+1)