Find the coefficient of `x^n` in the polynomial `(x+^n C_0)(x+3^n C_1)xx(x+5^n C_2)[x+(2n+1)^n C_n]dot`

Find the coefficient of x in polynomial (x+2n+1C_(0))(x+^(2n+1)C_(1))......(x+^(2n+1)C_(n))

The coefficient of x^(n) in the polynomial (x+""^(2n+1)C_(0))(X+""^(2n+1)C_(1)) (x+""^(2n+1)C_(2))……(X+""^(2n+1)C_(n)) is

If C_(0),C_(1), C_(2),...,C_(n) denote the cefficients in the expansion of (1 + x)^(n) , then C_(0) + 3 .C_(1) + 5 . C_(2)+ ...+ (2n + 1) C_(n) = .

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

The coefficient of x^(4) in the expansion of (1+x+x^(2)+x^(3))^(n) is *^(n)C_(4)+^(n)C_(2)+^(n)C_(1)xx^(n)C_(2)

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

If |x|<1, then the coefficient of x^(n) in expansion of (1+x+x^(2)+x^(3)+...)^(2) is n b.n-1 c.n+2 d.n+1

(1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + ...+ C_(n) x^(n) , show that sum_(r=0)^(n) C_(r)^(3) is equal to the coefficient of x^(n) y^(n) in the expansion of {(1+ x)(1 + y) (x + y)}^(n) .

The coefficient of x^(r)[0<=r<=(n-1)] in lthe expansion of (x+3)^(n-1)+(x+3)^(n-2)(x+2)+(x+3)^(n-3)(x+2)^(2)+...+(x+2)^(n) is ^(n)C_(r)(3^(r)-2^(n)) b.^(n)C_(r)(3^(n-r)-2^(n-r)) c.^(n)C_(r)(3^(r)+2^(n-r)) d.none of these