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study-the-sequence-u-n-1-u-n-ln-1-u-n-u-n-2-with-u-0-gt-0-




Question Number 33284 by abdo imad last updated on 14/Apr/18
study the sequence  u_(n+1)   = ((u_n  −ln(1+u_n ))/u_n ^2 )  with u_0 >0 .
$${study}\:{the}\:{sequence}\:\:{u}_{{n}+\mathrm{1}} \:\:=\:\frac{{u}_{{n}} \:−{ln}\left(\mathrm{1}+{u}_{{n}} \right)}{{u}_{{n}} ^{\mathrm{2}} } \\ $$$${with}\:{u}_{\mathrm{0}} >\mathrm{0}\:. \\ $$

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