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

Answers:

1. 6 3/8+ 8 1/4

Find the common denominator for 8 1/4 which is 8. Multiply by 2 for the numerator and denominator.

(1)(2)/(4)(2)=2/8

6 3/8+8 2/8

Answer : 14 5/8

4. 8 11/12-6 1/4

Find the common denominator for 6 1/4 which is 3. Multiply by 3 for the numerator and denominator.

(1)(3)/(4)(3)=3/12

8 11/12-6 3/12

= 2 8/12

Reduce the fraction. Divide by 4 for the numerator and denominator.

8/4=2 , 12/4=3

2 2/3