Question Number 33223 by prof Abdo imad last updated on 13/Apr/18
$${let}\:\:{A}_{{n}} \:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{e}^{{i}\pi{x}} }{\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+...{x}^{{n}−\mathrm{1}} }\:\:{with}\:{n}\geqslant\mathrm{3}\:{integr} \\ $$$${find}\:{the}\:{value}\:{of}\:{A}_{{n}} \:. \\ $$