If `alpha = e^(2pii/11)` and `f(x) = 5 + sum_(k=1)^60 A_ x^k`, then the value of `sum_(r=0)^10 f(alpha^r x)` is

If a=(e^(2 pi i))/(7) and f(x)=A_(0)+sum_(k=1)^(20)A_(k)x^(k) then the value of sum_(r=0)^(6)f(a^(r)x)=n(A_(0)+A_(n)x^(n)+A_(2n)x^(2n)), then the value of n is

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k=1)^(20)a_k x^k , then prove that the value of f(x)+f(alpha, x)++f(alpha^6x) is independent of alphadot

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k=0)^(20)a_k x^k , then prove that the value of f(x)+f(alpha x)+....+f(alpha^6x) is independent of alphadot

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k=0)^(20)a_k x^k , then prove that the value of f(x)+f(alpha x)+....+f(alpha^6x) is independent of alphadot

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k=0)^(20)a_k x^k , then prove that the value of f(x)+f(alpha x)+....+f(alpha^6x) is independent of alphadot

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k-0)^(20)a_k x^k , then prove that the value of f(x)+f(alpha, x)+......+f(alpha^6x) is independent of alphadot

If alpha=e^(i2 pi/7) and f(x)=a_(0)+sum_(k-0)^(20)a_(k)x^(k) then prove that the value of f(x)+f(alpha,x)+...+f(alpha^(6)x) is independent of alpha.

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

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