1×3分之1+3×5分之1+5×7分之1......+2009×2011分之1 +2011×2013分之1等于?
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1×3分之1+3×5分之1+5×7分之1+…+2009×2011分之1
=(1/2)*(1-1/3+1/3-1/5+1/5-1/7+.............+1/2009-1/2011)
=(1/2)*(1-1/2011)
=1005/2011
=(1/2)*(1-1/3+1/3-1/5+1/5-1/7+.............+1/2009-1/2011)
=(1/2)*(1-1/2011)
=1005/2011
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1/n(n+2)=[1/n-1/(n+1)]/2
1/1*3+1/3*5+。。。+1/2011*2013
=[1-1/3+1/3-1/5+1/5-.......+1/2009-1/2011+1/2011-1/2013]/2
=(1-1/2013)/2
=1006/2013
1/1*3+1/3*5+。。。+1/2011*2013
=[1-1/3+1/3-1/5+1/5-.......+1/2009-1/2011+1/2011-1/2013]/2
=(1-1/2013)/2
=1006/2013
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1/(1×3)+1/(3×5)+1/(5×7)+...+1/(2011×2013)
=1/2(1/1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+...+1/2(1/2011-1/2013)
=1/2×1-1/2×1/3+1/2×1/3-1/2×1/5+1/2×1/5-1/2×1/7+...+1/2×1/2011-1/2×1/2013
=1/2-1/2×1/2013
=1/2×(1-1/2013)
=1/2×2012/2013
=1006/2013
=1/2(1/1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+...+1/2(1/2011-1/2013)
=1/2×1-1/2×1/3+1/2×1/3-1/2×1/5+1/2×1/5-1/2×1/7+...+1/2×1/2011-1/2×1/2013
=1/2-1/2×1/2013
=1/2×(1-1/2013)
=1/2×2012/2013
=1006/2013
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