`C_(0)+C_(1)+C_(2)+......+C_(n)`=

If C_(0), C_(1), C_(2),C_(3),..., C_(n) are the binomial coefficients in the expansion of (C_(0))/(1)+(C_(2))/(3)+(C_(4))/(5)+(C_(6))/(7)+..., is equal to

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n) then for n odd ,C_(0)^(2)-C_(1)^(2)+C_(2)^(2)-C_(3)^(2)+...+(-1)C_(n)^(2), is equal to

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n) then 2C_(0)+(C_(1))/(2)+2^(3)(C_(2))/(3)+...+2^(n+1)(C_(n))/(n+1)=

If (1+x)^(n)=C_(0)+C_(1)x+C_(2)x^(2)+...+C_(n)x^(n) then the value of (C_(0))^(2)+((C_(1))^(2))/(2)+((C_(2))^(2))/(3)+...+((C_(n))^(2))/(n+1) is equal to

If C_(r) = ""^(n)C_(r) and (C_(0) + C_(1)) (C_(1) + C_(2)) … (C_(n-1) + C_(n)) = k ((n +1)^(n))/(n!) , then the value of k, is

if S_(n)=C_(0)C_(1)+C_(1)C_(2)+...+C_(n-1)C_(n) and (S_(n+1))/(S_(n))=(15)/(4) then n is

If C_(0),C_(1),C_(2),C_(3), . . .,C_(n) be binomial coefficients in the expansion of (1+x)^(n) , then Q. The value of the expression C_(0)+2C_(1) +3C_(2)+. . . .+(n+1)C_(n) is equal to

The mean of the values 0,1,2,3,... n,having corresponding weights C(n,0),C(n,1),C(n,2)......C(n,n) respectively is: