# 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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