Answer: B
Step-by-step explanation:
Step-by-step explanation:
f(x) = 1 / (5 + x)
Divide top and bottom by 5.
f(x) = ⅕ / (1 + ⅕x)
f(x) = ⅕ / (1 − (-⅕x))
Write as a geometric series.
f(x) = ∑ₙ₌₀°° ⅕ (-⅕x)ⁿ
f(x) = ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ xⁿ
f(x) = ∑ₙ₌₀°° (-1)ⁿ (⅕)ⁿ⁺¹ xⁿ
Use ratio test:
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(-1)ⁿ⁺¹ (⅕)ⁿ⁺² xⁿ⁺¹] / [(-1)ⁿ (⅕)ⁿ⁺¹ xⁿ]│< 1
lim(n→∞)│-1 (⅕) x│< 1
│x/5│< 1
│x│< 5
-5 < x < 5
If x = -5, ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ (-5)ⁿ = ∑ₙ₌₀°° ⅕ (1)ⁿ, which diverges.
If x = 5, ∑ₙ₌₀°° ⅕ (-1)ⁿ (⅕)ⁿ (5)ⁿ = ∑ₙ₌₀°° ⅕ (-1)ⁿ, which diverges.
The interval of convergence is therefore (-5, 5).
The answer would be B I hope this helps.
Answer:
36 ,36 30,2
Step-by-step explanation:
hope it's okay to you
Answer:
60 years
Step-by-step explanation: