How do you do both parts?

Step-by-step explanation:

f(x) = (4 + x) / (1 − x)

f(x) = (5 − (1 − x)) / (1 − x)

f(x) = 5 / (1 − x) − 1

Since ∑ₙ₌₀°° (xⁿ) = 1 / (1 − x), we can write f(x) as:

f(x) = 5 ∑ₙ₌₀°° (xⁿ) − 1

f(x) = 5 (1 + ∑ₙ₌₁°° (xⁿ)) − 1

f(x) = 5 + 5 ∑ₙ₌₁°° (xⁿ) − 1

f(x) = 4 + ∑ₙ₌₁°° 5(xⁿ)

Using ratio test:

lim(n→∞)│aₙ₊₁ / aₙ│< 1

lim(n→∞)│5(xⁿ⁺¹) / 5(xⁿ)│< 1

lim(n→∞)│x│< 1

│x│< 1

-1 < x < 1

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step-by-step explanation:

hopefully im right

answer: idk

step-by-step explanation: