let-u-0-x-o-and-u-n-1-ln-e-u-n-1-u-n-1-study-the-convervence-of-u-n-2-find-n-0-k-0-n-u-k-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 34313 by prof Abdo imad last updated on 03/May/18

let u_0 =x ≠o and u_(n+1) =ln(((e^u_n −1)/u_n )) 1) study the convervence of (u_n ) 2)find Σ_(n=0) ^∞ (Π_(k=0) ^n u_k ) .

$${let}\:{u}_{\mathrm{0}} ={x}\:\neq{o}\:\:{and}\:{u}_{{n}+\mathrm{1}} ={ln}\left(\frac{{e}^{{u}_{{n}} } \:−\mathrm{1}}{{u}_{{n}} }\right) \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{convervence}\:{of}\:\left({u}_{{n}} \right) \\ $$$$\left.\mathrm{2}\right){find}\:\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\left(\prod_{{k}=\mathrm{0}} ^{{n}} \:{u}_{{k}} \right)\:. \\ $$

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let-u-0-x-o-and-u-n-1-ln-e-u-n-1-u-n-1-study-the-convervence-of-u-n-2-find-n-0-k-0-n-u-k-

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