Step-by-step explanation:
(a) Fₙ₋₁ > 0, so Fₙ₊₁ > Fₙ. Each term is bigger than the one before it, so the function is increasing, meaning the series will diverge to infinity.
(b) Fₙ₊₁ / Fₙ = (Fₙ + Fₙ₋₁) / Fₙ
Divide.
Fₙ₊₁ / Fₙ = 1 + (Fₙ₋₁ / Fₙ)
Rewrite the second fraction using negative exponent.
Fₙ₊₁ / Fₙ = 1 + (Fₙ / Fₙ₋₁)⁻¹
Take the limit of both sides as n approaches infinity.
lim(n→∞) Fₙ₊₁ / Fₙ = 1 + lim(n→∞) (Fₙ / Fₙ₋₁)⁻¹
Substitute with φ.
φ = 1 + φ⁻¹
Solve.
φ² = φ + 1
φ² − φ − 1 = 0
φ = [ -(-1) ± √((-1)² − 4(1)(-1)) ] / 2(1)
φ = (1 ± √5) / 2
Since the ratio can't be negative:
φ = (1 + √5) / 2
Answer:
barbie
Step-by-step explanation:
ken
Answer:
The Black Stallion, known as the Black or Shêtân, is the title character from author Walter Farley's bestselling series about the Arab stallion and his young owner, Alec Ramsay. The series chronicles the story of a sheikh's prized stallion after he comes into Alec's possession, although later books furnish the Black's backstory. Shaytan (under various transliterations) is the Arabic word for "devil".
Answer:
100
Step-by-step explanation:
because if you add it all up you will find the sum
X² + 20x + 100 = 36⇒ x² + 20x + 100 - 36 = 0⇒ x² + 20x + 64 =0
Δ = b²-4ac = 20² -4·1·64 = 400-256 = 144
x₁= (-b+√Δ)/2a = (-20+√144)/2·1 = (-20+12)/2 = -8/2 = -4
x₂= (<span>-b-√Δ)/2a = (-20-√144)/2·1 = (-20-12)/2 = -32/2 = -16
x=-4 or x=-16</span>
