Interesting polynomial?

Calculus Level 4

Given that \(f(x) = x^n + x^{n-1} + x^{n-2} + \cdots + x^2 + x+ 1 \), evaluate the following:

\[\displaystyle \lim_{n\to\infty} \dfrac{\omega (\omega - 1) f'(\omega)}{n+5} \]

where \(\omega \) denotes a primitive \((n+1)^\text{th} \) root of unity.

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