If `1, a_r=1,2, 8` be `9^(th)` roots of unity , then `sum_(r=1)^8 1/a_r^5=`

If 1,alpha_(1),alpha_(2),.......... alpha_(2008) are (2009)^(th) roots of unity, then the value of sum_(r=1)^(2008)r(alpha_(r)+alpha_(2009-r)) equals

Let 1/(a_1+omega) + 1/(a_2+omega)+1/(a_3+omega)+ … . + 1/(a_n+omega)=i where a_1,a_2,a_3 …. a_n in R and omega is imaginary cube root of unity , then evaluate sum_(r=1)^(n)(2a_r-1)/(a_r^2-a_r+1) .

Let 1/(a_1+omega) + 1/(a_2+omega)+1/(a_3+omega)+ … . + 1/(a_n+omega)=i where a_1,a_2,a_3 …. a_n in R and omega is imaginary cube root of unity , then evaluate sum_(r=1)^(n)(2a_r-1)/(a_r^2-a_r+1) .

If 1,alpha,alpha^2,…,alpha^(n-1) are the n^(th) roots of unity show that sum_(r=1)^(n-1)r(alpha_r+alpha_(n-r))=-n .

Find sum_(r=1)^oo (-8) (-1/2)^r

If omega is a complex nth root of unity, then sum_(r=1)^n(ar+b)omega^(r-1) is equal to A.. (n(n+1)a)/2 B. (n b)/(1+n) C. (n a)/(omega-1) D. none of these

If omega is a complex nth root of unity, then sum_(r=1)^n(ar+b)omega^(r-1) is equal to A.. (n(n+1)a)/2 B. (n b)/(1+n) C. (n a)/(omega-1) D. none of these

If z_1,z_2,z_3,z_4 are imaginary 5th roots of unity, then the value of sum_(r=1)^(16)(z1r+z2r+z3r+z4r),i s 0 (b) -1 (c) 20 (d) 19

If z_1,z_2,z_3,z_4 are imaginary 5th roots of unity, then the value of sum_(r=1)^(16)(z1r+z2r+z3r+z4r),i s 0 (b) -1 (c) 20 (d) 19

Find: sum_(r=1)^oo (-8) (-1/2)^r