`" The sum of the series "3*C_(0)+11*C_(1)+19*C_(2)+27*C_(3)+...+(8n+3)*C_(n)" is "`

The sum of the series sum_(r=0) ^(n) ""^(2n)C_(r), is

If n is odd, then sum of the series C_(0)^(2)-C_(1)^(2)+C_(2)^(2)-C_(2)^(3)+…..+(-1)^(n)C_(n)^(2) is

.^(n) C_(2) + .^(7)C_(3) = .^(8) C_(3)

The sum of the series 1+(1)/(2) ""^(n) C_1 + (1)/(3) ""^(n) C_(2) + ….+ (1)/(n+1) ""^(n) C_(n) is equal to

If C_(r) stands for nC_(r), then the sum of first (n+1) terms of the series aC_(0)-(a+d)C_(1)+(a+2d)C_(2)-(a+3d)C_(3)+...... is

Find the sum C_(0)+3C_(1)+3^(2)C_(2)+...+3^(n)C_(n)

3C_(0)+5C_(1)+7C_(2)++(2n+3)C_(n)=2^(n)(n+3)