JEE Advanced Mathematics question
If is a nonreal cube root of unity then the value of
1·(2-ω)(2-ω^2)+2·(3-ω)(3-ω^2)++(n-1)(n-ω)(n-ω^2)
is
Answer: (A),(C)
Solution
The general term is for . Since and ,
(k-ω)(k-ω^2)=-(ω+ω^2)k+ω^3=+k+1,
(k-+k+1)=-1 .
Therefore
S=-1)=(-1)-(n-1)={
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