1-Prove-by-recurrence-that-so-n-N-and-R-cos-n-isin-n-cos-n-isin-n-2-Prove-that-U-n-1-1-5-U-n-2-6-and-U-1-5-2-is-decrease-

Tinku Tara June 4, 2023 Others 0 Comments

Question Number 158984 by LEKOUMA last updated on 11/Nov/21

1. Prove by recurrence that so n ∈ N and θ ∈ R (cos (nθ)+isin (nθ)=cos (nθ)+isin (nθ) 2. Prove that U_(n+1) =(1/5)(U_n ^2 +6) and U_1 =(5/2), is decrease

$$\mathrm{1}.\:{Prove}\:{by}\:{recurrence}\:{that}\: \\ $$$${so}\:\:{n}\:\in\:{N}\:{and}\:\theta\:\in\: {R}\: \\ $$$$\left(\mathrm{cos}\:\left({n}\theta\right)+{i}\mathrm{sin}\:\left({n}\theta\right)=\mathrm{cos}\:\left({n}\theta\right)+{i}\mathrm{sin}\:\left({n}\theta\right)\right. \\ $$$$\mathrm{2}.\:{Prove}\:{that}\:{U}_{{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{5}}\left({U}_{{n}} ^{\mathrm{2}} +\mathrm{6}\right)\:{and} \\ $$$${U}_{\mathrm{1}} =\frac{\mathrm{5}}{\mathrm{2}},\:{is}\:{decrease} \\ $$$$ \\ $$

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1-Prove-by-recurrence-that-so-n-N-and-R-cos-n-isin-n-cos-n-isin-n-2-Prove-that-U-n-1-1-5-U-n-2-6-and-U-1-5-2-is-decrease-

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