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Prove that (C1)/2+(C3)/3+(C5)/6+=(2^(n+1...

Prove that `(C_1)/2+(C_3)/3+(C_5)/6+=(2^(n+1)-1)/(n+1)dot`

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`S = (.^(n)C_(1))/(2)+(.^(n)C_(3))/(4)+(.^(n)C_(5))/(6)+"..."`
`:. T_(r) = (.^(n)C_(2r-1))/(2r)= (.^(n+1)C_(2r))/(n+1)`, where `r = 1,2,3,"...."`
`rArr S = 1/(n+1)(.^(n+1)C_(2)+.^(n+1)C_(4)+.^(n+1)C_(6)+"....")`
` = (1)/(n+1)[(.^(n+1)C_(0) + .^(n+1)C_(2) + .^(n+1)C_(4) +"....")-.^(n+1)C_(0)] = (2^(n)-1)/(n+1)`.
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