If `(1+x)^(15)=C_(0)+C_(1)x+C_(2)x^(2)+....+C_(15^(x^(15)))`, then find the sum of `2 C_(2)+2.3 C_(3)+3.4 C_(4)+….+14.15 C_(15)`

Find the sum C_(0)-C_(2) +C_(4)-C_(6)+…. , where C_(r)=^(n)C_(r)

If ""^(18)C_(15)+2(""^(18)C_16))+""^(17)C_(16)+1=""^(n)C_(3) , then n is equal to :

If (1+x)^(n) = overset(n)underset(r=0)Sigma C_(r)x^(r ) , then prove that C_(1)+2C_(2)+3C_(3)+…..+nC_(n)=n2^(n-1) .

Find the sum 3^(n)C_(0)-8^(n)C_(1)+13^(n)C_(2)-18 xx ^(n)C_(3)+…

If C_(0),C_(1),C_(2),...,C_(15) are binomial coefficients in (1+x)^(15) , then C_(1)/(C_(0))+2C_(2)/(C_(1))+3C_(3)/(C_(2))+...+15C_(15)/(C_(14)) is equal to

Find the sum of the series ""^(15)C_(0)+^(15)C_(1)+^(15)C_(2)+….+^(15)C_(7) .

If ""^(n)C_(2) + ""^(n)C_(3) = ""^(6)C_(3) and ""^(n)C_(x) = ""^(n)C_(3), x != 3 , then the value of x is