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Question Number 40125 by maxmathsup by imad last updated on 16/Jul/18
$${let}\:{z}_{\mathrm{0}} =\mathrm{0}\:\:{and}\:\:\forall{n}\:\in{N}\:\:\:{z}_{{n}+\mathrm{1}} =\frac{{i}}{\mathrm{2}}{z}_{{n}} \:+\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:\:{find}\:\:{z}_{{n}} {at}\:{form}\:{of}\:{sum} \\ $$$$\left.\mathrm{2}\right){let}\:{W}_{{n}} \:\:={z}_{{n}} \:\:\:\:−\frac{\mathrm{1}+{i}}{\mathrm{2}}\:\:\:{find}\:{lim}\:\mid{W}_{{n}} \mid\left({n}\rightarrow+\infty\right) \\ $$