1/2*3+31/3*5...1/9*11

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1/2*3+31/3*5...1/9*11

1/2*3+31/3*5...1/9*11
1/2*3+31/3*5...1/9*11

1/2*3+31/3*5...1/9*11
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应该为:
1/2*3+1/3*5...1/9*11
=(1/2-1/3)+(1/2)【(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)】
=1/6+(1/2)(1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/6+(1/2)(1/3-1/11)
=1/6+8/33
=35/66

1/(1×3)+1/(3×5)+……+1/(9×11)
=1/2(1-1/3)+1/2(1/3-1/5)+……+1/2(1/9-1/11)
=1/2[(1-1/3)+(1/3-1/5)+……+(1/9-1/11)]
=1/2(1-1/3+1/3-1/5+……+1/9-1/11)
=1/2(1-1/11)
=1/2×10/11
=5/11
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1/(1×3)+1/(3×5)+……+1/(9×11)
=1/2(1-1/3)+1/2(1/3-1/5)+……+1/2(1/9-1/11)
=1/2[(1-1/3)+(1/3-1/5)+……+(1/9-1/11)]
=1/2(1-1/3+1/3-1/5+……+1/9-1/11)
=1/2(1-1/11)
=1/2×10/11
=5/11

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