If `(4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r)`, then the value of

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

If n in N such that is not a multiple of 3 and (1+x+x^(2))^(n) = sum_(r=0)^(2n) a_(r ). X^(r ) , then find the value of sum_(r=0)^(n) (-1)^(r ).a_(r).""^(n)C_(r ) .

If (1-x^(2))^(n)=sum_(r=0)^(n)a_(r)x^(r)(1-x)^(2n-r), then a_(r) is equal to ^(n)C_(r) b.^(n)C_(r)3^(r) c.^(2n)C_(r) d.^(n)C_(r)2^(r)

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

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

If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a_(r)x^(r)(1-x)^(3n-2r) , then the value of a_(r) , where n in N is

If (1-x^(3))^(n)=underset(r=0)overset(n)(sum)a_(r)x^(r)(1-x)^(3n-2r) , then the value of a_(r) , where n in N is

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

(1+x)(sum_(r=0)^(n)nC_(r)x^(r))+(1+x^(2))(sum_(r=0)^(n-1)(n-1)C_(r)x^(r))+...(1+x^(n))(sum_(r=0)^(1)1C_(r)x^(r))=a_(0)+a_(1)x+, then the value of (a_(1))/(a_(n)+1)+(a_(1))/(a_(n))+(a_(2))/(a_(n-1))+......+(a_(n+1))/(a_(0)) is equal to