`15C_0+15C_1+15C_2+..................+15C_15=`

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

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

^(15)C_3 + ^(15)C_5 + ....+ ^(15)C_15 =

With usual notations prove that C_1/C_0 + 2. C_2/C_1 + 3.C_3/C_2 + ……+n.(C_n)/(C_(n-1)) = (n(n +1))/(2) Hence prove that (15C_1)/(15C_0) + 2.(15C_2)/(15C_1) + 3. (15C_3)/(15C_2) +……..+ 15. (15C_15)/(15C_14) = 120

With usual notations prove that C_1/C_0 + 2. C_2/C_1 + 3.C_3/C_2 + ……+n.(C_n)/(C_(n-1)) = (n(n +1))/(2) Hence prove that (15C_1)/(15C_0) + 2.(15C_2)/(15C_1) + 3. (15C_3)/(15C_2) +……..+ 15. (15C_15)/(15C_14) = 120

Value of -^(15)C_(1) + 2..^(15)C_(2)- 3.^(15)C_(3) + ...... - 15.^(15)C_(15)+ ^(15)C_(1)+ ^(15)C_(2)+ ....^(15)C_(14) is

The value of : ^15C_1 +^15C_3 + ^15C_5+…..+ ^15C_15 is

15C_(3)+^(15)C_(5)+........+^(15)C_(15) will be equal to

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

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