Find the sum `^20C_10.^15C_0+^20C_9.^15C_1+^20C_8.^15C_2+....+^20C_0.^15C_10`

Find the sum sum_(k=0)^(10).^(20)C_k .

Find the sum of the series .^15 C_0+^(15)C_1+^(15)C_2+...............+^(15)C_7 .

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

The value of .^(15)C_(0)^(2)-.^(15)C_(1)^(2)+.^(15)C_(2)^(2)-"...."-.^(15)C_(15)^(2) is a. 15 b. -15 c. 0 d. 51

The sum of the series ""^20C_0 - ""^20C_1 + ""^20C_2 - ""^20C_3 +…….""^20C_10 is

The sum of the series .^(20)C_(0)-.^(20)C_(1)+ .^(20)C_(2)-.^(20)C_(3)+...-.+ .^(20)C_(10) is -

Find the value of (.^(10)C_(10))+(.^(10)C_(0)+.^(10)C_(1))+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2))+"...."+(.^(10)C_(0)+.^(10)C_(1)+.^(10)C_(2)+"....." + .^(10)C_(9)) .

The sum of the series ""^20 C_0-""^20 C_1+""^20C_2-""^20C_3+...-...+""^20C_10 is:

prove that sum_(k=0)^10 20^C_k=2^(19)

C_0^2 -C_1^2 + C_2^2 - ………-C_15^2 =