If `(1+x)^(15)=C_0+C_1x+C_2x^2++C_(15)x^(15),` then find the su of `C_1+2C_3+3C_4++14 C_(15)dot`

If (1+x)^(15)=C_0+C_1x+C_2x^2++C_(15)x^(15), then find the value of C_2+2C_3+3C_4++14 C_(15)dot

If (1 + x)^(n) = C_(0) + C_(1) x C_(2) x^(2) +…+ C_(n) x^(n) , then the sum C_(0) + (C_(0)+C_(1))+…+(C_(0) +C_(1) +…+C_(n -1)) is equal to

If (1+x)^n = C_0 + C_1x + C_2x^2 + ……..+C_n.x^n then find C_1 - C_3 + C_5 + ……

If (1+x)^n = C_0 + C_1x + C_2x^2 + ……..+C_n.x^n then find C_0 - C_2 + C_4 - C_6 + …….

If ""^(15)C_(x)=""^(15)C_(x+3) , then find the value of X.

If (1+x)^(2010)=C_(0)+C_(1)x+C_(2)x^(2)+ …….+C_(2010) x^(2010) then the sum of series C_(2)+C_(5)+C_(8)+ ……… +C_(2009) equals to :

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + …+ C_(n) x^(n) , then for n odd, C_(1)^(2) + C_(3)^(2) + C_(5)^(2) +....+ C_(n)^(2) is equal to

C_0^2 -C_1^2 + C_2^2 - ………-C_15^2 =

If (1 + x - 2 x^(2))^(6) = 1 + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(12) x^(12) , then the value of C_(2) + C_(4) + C_(6) + …+ C_(12) is

If (1+x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + "….." + C_(n)x^(n) , then C_(0) - (C_(0) + C_(1)) +(C_(0) + C_(1) + C_(2)) - (C_(0) + C_(1) + C_(2) + C_(3))+ "….." (-1)^(n-1) (C_(0) + C_(1) + "……" + C_(n-1)) is (where n is even integer and C_(r) = .^(n)C_(r) )