Question Number 178468 by Huy last updated on 16/Oct/22
$${For}\:{the}\:{sequence}\:\left\{{u}_{{n}} \right\}\:{if}\:{u}_{\mathrm{1}} =\mathrm{1},\:{u}_{\mathrm{2}} =\mathrm{2}\:{and}\:{u}_{{n}+\mathrm{2}} ^{\mathrm{2}} ={u}_{{n}} ^{\mathrm{2}} +{u}_{{n}+\mathrm{1}} ^{\mathrm{2}} −{u}_{{n}} {u}_{{n}+\mathrm{1}} ,\:{for}\:{all}\:{natural}\:{number}\:{n}. \\ $$$${Find}\:{lim}\:{u}_{{n}} ? \\ $$