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Evaluate the following sum in terms of nnn,
∑k=1n(k+1)(k+1ω)(k+1ω2)\displaystyle \sum_{k=1}^n (k+1)\left(k + \dfrac{1}{\omega}\right)\left(k + \dfrac{1}{\omega^2}\right)k=1∑n(k+1)(k+ω1)(k+ω21)
Notations: ω\omegaω and ω2\omega^2ω2 are non-real cube roots of unity.
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