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Question Number 34313 by prof Abdo imad last updated on 03/May/18
$${let}\:{u}_{\mathrm{0}} ={x}\:\neq{o}\:\:{and}\:{u}_{{n}+\mathrm{1}} ={ln}\left(\frac{{e}^{{u}_{{n}} } \:−\mathrm{1}}{{u}_{{n}} }\right) \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{convervence}\:{of}\:\left({u}_{{n}} \right) \\ $$$$\left.\mathrm{2}\right){find}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\left(\prod_{{k}=\mathrm{0}} ^{{n}} \:{u}_{{k}} \right)\:. \\ $$