Question Number 30550 by abdo imad last updated on 23/Feb/18
$${let}\:{f}\left({z}\right)=\:\sum_{{n}\geqslant\mathrm{0}} {a}_{{n}} {z}^{{n}} \:\:\:/{a}_{\mathrm{0}} =\mathrm{1}\:,{a}_{\mathrm{1}} =\mathrm{3}\:{and}\:\forall{n}\geqslant\mathrm{2} \\ $$$${a}_{{n}} =\mathrm{3}{a}_{{n}−\mathrm{1}} −\mathrm{2}\:{a}_{{n}−\mathrm{2}} \:\:\:\:{find}\:{f}\left({z}\right)\:{for}\:\mid{z}\mid<\mathrm{1}\:\:\left({z}\in{C}\right)\:. \\ $$