Question Number 30501 by abdo imad last updated on 22/Feb/18
$${let}\:{put}\:{w}={e}^{{i}\frac{\mathrm{2}\pi}{{n}}} \:\:\:\:\:{find}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\left({x}+{w}^{{k}} \right)^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} {n}\left({x}+{w}^{{k}} \right)^{{n}−\mathrm{1}} \:\:. \\ $$$$ \\ $$