Evaluate the sum (1 + 1/ω) + (1 + 1/ω^2) + (2 + 1/ω) + (2 + 1/ω^2) + (3 + 1/ω) + (3 + 1/ω^2) + ... + (n + 1/ω) + (n + 1/ω^2), where ω is an imaginary cube root of unity.

Question

Accepted Answer

n(n^2 + 2)/3. The correct option is derived from recognizing that the sum consists of terms that can be grouped based on the properties of the imaginary cube roots of unity, which simplify the calculations. Each group contributes a consistent value, leading to the final result of n(n^2 + 2)/3.

Evaluate the sum (1 + 1/ω) + (1 + 1/ω^2) + (2 + 1/ω) + (2 + 1/ω^2) + (3 + 1/ω) + (3 + 1/ω^2) + ... + (n + 1/ω) + (n + 1/ω^2), where ω is an imaginary cube root of unity.

Solution

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