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If `underset(i=1)overset(20)Sigma((.^(20)C_(i-1))/(.^(20)C_(i)+.^(20)C_(i-1)))^(3)=(k)/(21)`, then k equals

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`(""^10C_(i-1) )/(""^10C_i + ""^10C_(i-1) ) = (""^10C_(i-1) )/(""^11C_i)`
`( (10!)/((10 - I + 1 ) !(i-1)!))/((11!)/((11 - i)!i!)) = (10!)/((10 - i+ 1) (i-1)!) xx ((11-i)!i!)/(11!)`
` sum_(i=1)^(10) (i^3)/(11^3) = (k)/(11) , (10^2 xx 11^2)/(4 xx 10^3) =(k)/(11)`
k = 25
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