For-the-sequence-u-n-if-u-1-1-u-2-2-and-u-n-2-2-u-n-2-u-n-1-2-u-n-u-n-1-for-all-natural-number-n-Find-lim-u-n-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 178468 by Huy last updated on 16/Oct/22

For the sequence {u_n } if u_1 =1, u_2 =2 and u_(n+2) ^2 =u_n ^2 +u_(n+1) ^2 −u_n u_(n+1) , for all natural number n. Find lim u_n ?

$${For}\:{the}\:{sequence}\:\left\{{u}_{{n}} \right\}\:{if}\:{u}_{\mathrm{1}} =\mathrm{1},\:{u}_{\mathrm{2}} =\mathrm{2}\:{and}\:{u}_{{n}+\mathrm{2}} ^{\mathrm{2}} ={u}_{{n}} ^{\mathrm{2}} +{u}_{{n}+\mathrm{1}} ^{\mathrm{2}} −{u}_{{n}} {u}_{{n}+\mathrm{1}} ,\:{for}\:{all}\:{natural}\:{number}\:{n}. \\ $$$${Find}\:{lim}\:{u}_{{n}} ? \\ $$

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For-the-sequence-u-n-if-u-1-1-u-2-2-and-u-n-2-2-u-n-2-u-n-1-2-u-n-u-n-1-for-all-natural-number-n-Find-lim-u-n-

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