C_(0)+2.C_(1)+3.C_(2)+....+(n+1)C_(n)=

If the value of C_(0)+2C_(1)+3C_(2)+ . . .+(n+1)C_(n)=576 , then n is

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(r) then prove that C_(0)+2C_(1)+3C_(2)+.....+(n+1)C_(n)=2^(n-1)(n+2)

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

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

If C_(0),C_(1),C_(2)…….,C_(n) are the combinatorial coefficient in the expansion of (1+x)^n, n, ne N , then prove that following C_(1)+2C_(2)+3C_(3)+..+n.C_(n)=n.2^(n-1) C_(0)+2C_(1)+3C_(2)+......+(n+1)C_(n)=(n+2)C_(n)=(n+2)2^(n-1) C_(0),+3C_(1)+5C_(2)+.....+(2n+1)C_n =(n+1)2^n (C_0+C_1)(C_1+C_2)(C_2+C_3)......(C_(n-1)+C_n)=(C_0.C_1.C_2....C_(n-1)(n+1)^n)/(n!) 1.C_0^2+3.C_1^2+....+ (2n+1)C_n^2=((n+1)(2n)!)/(n! n!)

Find the sum 1C_(0)+2C_(1)+3C_(2)+...+(n+1)C_(n), where C_(r)=^(n)C_(r)

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) +… + C_(n) x^(n) , prove that C_(0) + 2C_(1) + 3C_(2) + …+ (n+1)C_(n) = (n+2)2^(n-1) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) +… + C_(n) x^(n) , prove that C_(0) + 2C_(1) + 3C_(2) + …+ (n+1)C_(n) = (n+2)2^(n-1) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) +… + C_(n) x^(n) , prove that C_(0) + 2C_(1) + 3C_(2) + …+ (n+1)C_(n) = (n+2)2^(n-1) .

If (1+x)^(n)=C_(0)+C_(1).x+C_(2).x^(2)+….+C_(n).x^(n). then prove that (i) C_(0)+2C_(1)+3C_(2)+…+(n-1)C_(n)=(n+2).2^(n-1) (ii)C_(0)+3C_(1)+5C_(2)+...+(2n+1)C_(n)=(n+1).2^(n)