If `f(x)=sum_(k=0)^n a_k |x-1|^k`, where `a_i in R`, then

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=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 f(x) = sum_(k=2)^(n) (x-(1)/(k-1))(x-(1)/(k)) , then the product of root of f(x) = 0 as n rarr oo , is

If f(x) =Pi_(i=1)^3(x-a_i) + sum_(i=1)_3 a_i - 3x where a_i < a_(i+1) for i = 1,2, then f(x) = 0 have

If f(x) =Pi_(i=1)^3(x-a_i) + sum_(i=1)_3 a_i - 3x where a_i < a_(i+1) for i = 1,2, then f(x) = 0 have

If sum_(k=0)^(n) f (x+ka)=0 where a gt 0 then the period of f(x) is a)a b)(n+1) a c) a/(n+1) d)f(x) is non - periodic

Let (1+x^2)^2(1+x)^n=sum_(k=0)^(n+4)a_k x^k . If a_1 , a_2 and a_3 are in arithmetic progression, then the possible value/values of n is/are a. 5 b. 4 c. 3 d. 2