(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)

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(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
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(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)

(求和)1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
1/2+1/6=2/3
1/2+1/6+1/12=3/4
1/2+1/6+1/12+1/20=4/5
.
所以
1/(1×2)+1/(2×3)+1/(3×4)+……+1/(2011×2012)
=2011/2012

2011/2012

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

2011/2012

1/n(n+1)=1/n-1/(n+1)
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