Question

02. Să se determine X2, X3, X4 in functie de Xn
Urgent va rog, dau coroană!

Answer 1

Răspuns:

Explicație pas cu pas:

a) x₁ = 0 ; xₙ₊₁ = 5xₙ+3  ; n ≥ 1

x₂ = 5x₁+3 = 5·0+3 = 3

x₃ = 5x₂+3 = 5·3+3 = 18

x₄ = 5x₃+3 = 5·18+3 = 93

b) x₁ = √5 ; xₙ₊₁ = √(5+xₙ)

x₂ = √(5+√5)

x₃ = √[5+√(5+√5)]

x₄ = √{5+√[5+√(5+√5)]}

c) x₁ = 2 ; xₙ = 1/2 ·xₙ₋₁ + 1 ; n ≥ 2

x₂ = 1/2 ·x₁ +1 = 1/2 ·2 + 1 = 1+1 = 2

x₃ = 1/2 ·x₂+1 =  1/2 ·2 + 1 = 1+1 = 2

x₄ = 1/2 ·x₃+1 =  1/2 ·2 + 1 = 1+1 = 2

d) x₁ = 0 ; xₙ - xₙ₋₁ = (1/2)ⁿ⁺¹ ; n ≥ 2

x₂ = x₁+(1/2)²⁺¹ = 0 + 1/2³ = 1/8

x₃ = x₂+(1/2)⁴ = 1/8 + 1/16 = 3/16

x₄ = x₃+(1/2)⁵ = 3/16+1/32 = 7/32

e) x₁ = 1/2 ; xₙ₊₁ = xₙ/(1+2xₙ) ; n≥ 1

x₂ = x₁ / (1+2x₁) = 1/2 / (1+1) = 1/4

x₃ = x₂/(1+2x₂) = 1/4 / (1+1/2) = 1/4 / 3/2 = 1/4 ·2/3 = 2/12 = 1/6

x₄ = x₃/(1+2x₃) = 1/6 / (1+1/3) = 1/6 / 4/3 = 1/6 · 3/4 = 3/24 = 1/8

f) x₁ = 3/2 ; xₙ = n / (n+2) ·xₙ₋₁ ; n ≥ 2

x₂ = 2/(2+2) ·3/2 = 1/2 ·3/2 = 3/4

x₃ = 3/(3+2) ·3/4 = 3/5 ·3/4 = 9/20

x₄ = 4(4+2) ·9/20 = 2/3 ·9/20 = 18/60 = 3/10