[" If "C_(0),C_(2),C_(4),....." are the binomial "],[" coefficients in the expansion of "(1+x)^(9)],[" then "C_(0)+C_(2)+C_(4)+C_(6)+C_(8)=]

If C_(0),C_(1),C_(2),........C_(n), are the Binomial coefficients in the expansion of (1+x)^(n),n being even,then C_(0)+(C_(0)+C_(1))+(C_(0)+C_(1)+C_(2))+....+(C_(0)+C_(1)+C_(2)+......+C_(n) is equal to

If C_0, C_2, C_4,….. are the binomial coefficient in the expansion of (1+x)^9 then C_0+C_2 +C_4+ C_6+ C_8=

If C_(0),C_(1),C_(2),…,C_(n) are the binomial coefficients in the expansion of (1+x)^(n)*n being even, then C_(0)+(C_(0)+C_(1))+(C_(0)+C_(1)+C_(2))+….+(C_(0)+C_(1)+C_(2)+…+C_(n-1)) is equal to :

If C_(0),C_(1),C_(2),…,C_(n) are the binomial coefficients in the expansion of (1+x)^(n)*n being even, then C_(0)+(C_(0)+C_(1))+(C_(0)+C_(1)+C_(2))+….+(C_(0)+C_(1)+C_(2)+…+C_(n-1)) is equal to :

" if" C_(0)C_(1)C_(2),……C_(n) are the binomial coefficients in the expansion of (1+x)^(n) then prove that: C_(0)C_(2)+C_(1)C_(3)+C_(2)C_(4)+……+C_(n-2)C_(n)=(|ul2n)/(|uln-2|uln+2)

" if" C_(0)C_(1)C_(2),……C_(n) are the binomial coefficients in the expansion of (1+x)^(n) then prove that: C_(0)C_(2)+C_(1)C_(3)+C_(2)C_(4)+……+C_(n-2)C_(n)=(|ul2n)/(|uln-2|uln+2)

If C_(0), C_(1), C_(2), C_(3),.., C_(n) are the binomial coefficients in the expansion of (1+x)^(n) , then (C_(0))/(1)+(C_(2))/(3)+(C_(4))/(5)+(C_(6))/(7)+...... =

If C_(0), C_(1), C_(2),..., C_(n) denote the binomial coefficients in the expansion of (1 + x)^(n) , then . 1^(2). C_(1) - 2^(2) . C_(2)+ 3^(2). C_(3) -4^(2)C_(4) + ...+ (-1).""^(n-2)n^(2)C_(n)= .