let-c-0-gt-0-and-n-N-c-n-1-1-2-c-n-1-c-n-Explicit-c-n-in-term-of-n-and-c-0-

Tinku Tara June 4, 2023 Differentiation 0 Comments

Question Number 83139 by ~blr237~ last updated on 28/Feb/20

let c_0 >0 and ∀ n∈N c_(n+1) =(√((1/2)(c_n +(1/c_n ) ) )) Explicit c_n in term of n and c_0

$${let}\:\:\:{c}_{\mathrm{0}} \:>\mathrm{0}\:\:{and}\:\:\forall\:{n}\in\mathbb{N}\:\:{c}_{{n}+\mathrm{1}} =\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\left({c}_{{n}} +\frac{\mathrm{1}}{{c}_{{n}} }\:\right)\:}\:\:\: \\ $$$${Explicit}\:\:{c}_{{n}} \:{in}\:{term}\:{of}\:{n}\:{and}\:\:{c}_{\mathrm{0}} \:\: \\ $$

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let-c-0-gt-0-and-n-N-c-n-1-1-2-c-n-1-c-n-Explicit-c-n-in-term-of-n-and-c-0-

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