If `alpha_(0),alpha_(1),alpha_(2),...,alpha_(n-1)` are the n, nth
roots of the unity , then find the value of `sum_(i=0)^(n-1)(1)/(2-a_(i)).`

If 1,alpha_(1),alpha_(2),alpha_(3),...,alpha_(n-1) are n, nth roots of unity, then (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))...(1-alpha_(n-1)) equals to

If z_(1),z_(2),z_(3),…………..,z_(n) are n nth roots of unity, then for k=1,2,,………,n

If 1,omega,omega^(2),...omega^(n-1) are n, nth roots of unity, find the value of (9-omega)(9-omega^(2))...(9-omega^(n-1)).

Consider (1 + x + x^(2))^(n) = sum_(r=0)^(n) a_(r) x^(r) , where a_(0), a_(1), a_(2),…, a_(2n) are real number and n is positive integer. If n is odd , the value of sum_(r-1)^(2) a_(2r -1) is

Consider (1 + x + x^(2))^(n) = sum_(r=0)^(n) a_(r) x^(r) , where a_(0), a_(1), a_(2),…, a_(2n) are real number and n is positive integer. The value of sum_(r=0)^(n-1) a_(r) is

If alpha and beta is the root of the equation x^2-3x+2=0 then find the value of alpha^2 + beta^2

If alpha,beta be the roots of the equation 3x^2+2x+1=0, then find value of ((1-alpha)/(1+alpha))^3+((1-beta)/(1+beta))^3

If Sigma_(i=1)^(2n) cos^(-1) x_(i) = 0 ,then find the value of Sigma_(i=1)^(2n) x_(i)

If alpha_(1), alpha_(2), alpha_(3), beta_(1), beta_(2), beta_(3) are the values of n for which sum_(r=0)^(n-1)x^(2r) is divisible by sum_(r=0)^(n-1)x^(r ) , then the triangle having vertices (alpha_(1), beta_(1)),(alpha_(2),beta_(2)) and (alpha_(3), beta_(3)) cannot be

Find the sum of n terms of the series whose nth terms is (i) n(n-1)(n+1) .