`C_1/2+C_3/4+............+C_15/16=`

15C_(0)+15C_(1)+15C_(2)+...............+15C_(15)=

Evaluate the following : ""^16C_1+""^16C_3+""^16C_5+ ....... +""^16C_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 .

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

If for z as real or complex, (1+z^2+z^4)^8=C_0+C_1z^2+C_2z^4+...+C_(16)z^(32) then prove that C_(0) - C_(1) + C_(2) - C_(3) + "….." + C_(16) = 1 and C_(0) + C_(3) + C_(6) + C_(12) + C_(15) = 3^(7)

16C_(0)-16C_(1)+16C_(2)-..........+16C_(8)

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