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

Find the sum 3^n C_0-8^n C_1+13^n C_2 - 18^n C_3+..

Find the sum 1.^(n)C_(0) + 3 .^(n)C_(1) + 5.^(n)C_(2) + "….." + (2n+1).^(n)C_(n) .

Find the value of ^20 C_0-(^(20)C_1)/2+(^(20)C_2)/3-(^(20)C_3)/4+dot

Prove that (^n C_0)/1+(^n C_2)/3+(^n C_4)/5+(^n C_6)/7+.....+dot=(2^n)/(n+1)dot

Find the sum 1C_0+2C_1+3C_2++(n+1)C_n ,w h e r eC_r=^n C_rdot

C_(1) + 4.C_(2) + 7.C_(3) +......+(3n - 2).C_(n) =

Find the value of .^(20)C_(0) xx .^(13)C_(10) - .^(20)C_(1) xx .^(12)C_(9) + .^(20)C_(2) xx .^(11)C_(8) - "……" + .^(20)C_(10) .

The value of sum_(r=0)^(10)(r)^(20)C_r is equal to: a. 20(2^(18)+^(19)C_(10)) b. 10(2^(18)+^(19)C_(10)) c. 20(2^(18)+^(19)C_(11)) d. 10(2^(18)+^(19)C_(11))

Find the sum of the series ^15 C_0+^(15)C_1+^(15)C_2++^(15)C_7dot