verify that `C(15,8)+C(15,9)-C(15,6)-C(15,7)=0`

Verify that: (i) .^(15)C_(8)+.^(15)C_(9)-.^(15)C_(7)=0 " " (ii) .^(10)C_(4)+.^(10)C_(3)=.^(11)C_(4)

((15),(8))+((15),(9))-((15),(6))-((15),(7))=......

Prove that , .^(15)C_(8)+^(15)C_(9)-.^(15)C_(6)-^(15)C_(7)=0

The value of 0fC(15,0)^(2)-C(15,1)^(2)-C(15,2)^(2)-...-C(15,15)^(2)

Prove that , .^15C_8+.^15C_9-.^15C_6-.^15C_7=0

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

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

Find the sum of the series quad 15C_(0)+^(15)C_(1)+^(15)C_(2)++^(15)C_(7)