If `(1+x+x^2+x^3)^n=sum_(r=0)^(3n)b_r x^r and sum_(r=0)^(3n)b_r=k ,"t h e n"sum_(r=0)^(3n)r b_r` is

If (1+x+x^(2)+x^(3))^(n)=sum_(r=0)^(3n)b_(r)x^(r) and sum_(r=0)^(3n)b_(r)=k, the n sum_(r=0)^(3n)rb_(r)

Let (1 + x + x^(2))^(n) = sum_(r=0)^(2n) a_(r) x^(r) . If sum_(r=0)^(2n)(1)/(a_(r))= alpha , then sum_(r=0)^(2n) (r)/(a_(r)) =

If (1+x)^(n)=sum_(r=0)^(n)C_(r)x^(n) and sum_(r=0)^(n)(C_(r))/(r+1)=k then the value of k is

sum_(r=1)^(n)(3^(r)-r)=

If ninN,ngt4 and (1-x^(3))^(n)=sum_(r=0)^(n)a_(r)x^(r)(1-x)^(3n-2r) , then sum_(r=0)^(n)a_(r)=lambda^(n) , find lambda.