Complexity! (7)
Algebra
Level
4
Evaluate the following sum in terms of \(n\),
\[\displaystyle \sum_{k=1}^n (k+1)\left(k + \dfrac{1}{\omega}\right)\left(k + \dfrac{1}{\omega^2}\right)\]
Notations: \(\omega\) and \(\omega^2\) are non-real cube roots of unity.
For more problems on complex numbers, click here.
by
Tapas Mazumdar