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Prove that (^n C0)/1+(^n C2)/3+(^n C4)/5...

Prove that `(^n C_0)/1+(^n C_2)/3+(^n C_4)/5+(^n C_6)/7+.....+dot=(2^n)/(n+1)dot`

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`S = (.^(n)C_(0))/(1)+(.^(n)C_(2))/(3)+(.^(n)C_(4))/(5)+(.^(n)C_(6))/(7)+"….."`
The general term of the series in
`(.^(n)C_(2r))/(2r+1) = (.^(n+1)C_(2r+1))/(n+1)`, where `r = 0,1,2,"….."`
`:. S = (1)/(n+1)[.^(n+1)C_(1)+.^(n+1)C_(3)+.^(n+1)C_(5)+"......."] = (2^(n))/(n+1)`
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