Find the sum `2C_0(2_3)/2C_1+(2^3)/3C_2+(2^4)/4C_3++(2^(11))/(11)C_(10)dot`

2C_(0)+(2^(2))/(2)C_(1)+(2^(3))/(3)C_(2)+..........+(2^(11))/(11)C_(10)=?

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

Find the sum 2..^(10)C_(0) + (2^(2))/(2).^(10)C_(1) + (2^(3))/(3).^(10)C_(2)+(2^(4))/(4).^(10)C_(3)+"...."+(2^(11))/(11).^(10)C_(10) .

(C_(0))/(2)+(C_(1))/(3)+(C_(2))/(4)+...+(C_(8))/(10)

If C_r stands for ^10C_r show that 2.C_0+2^2/2.C_1+2^3/3.C_2+…+2^11/11.C_10= (3^11-1)/11)

If (1+x)^n=C_0+C_1x+C_2x^2+C_3x^3+...+C_nx^n then prove that 2.C_0+2^2C_1/2+2^3C_2/3+2^4C_3/4+...+2^(n+1)C_n/(n+1)=(3^(n+1)-1)/(n+1)

Evaluate : 2^(10)C_(0)+(2^(2).^(10)C_(1))/(2)+(2^(3).^(10)C_(2))/(3)+ . . .+(2^(11).^(10)C_(10))/(11)

(C_(0))^(2)+2(C_(1))^(2)+3(C_(2))^(2)+4(C_(3))^(2)...+(n+1)(c_(n))^(2)