Chapter 1 Text work review

10. S\( _\infty \) = 2t₁. r = ?

S\( _\infty \) = 2t₁ = \( \frac{t_1}{1 - r} \)

2(1 - r) = 1

2 - 2r = 1

2r = 1

r = 0.5

11. For what values of x will each series be convergent?

a) 5 + 5x + 5x² + 5x³ + ...

r = x, t₁ = 5

-1 < x < 1

b) 1 + \( \frac{x}{3} \) + \( \frac{x^2}{9} \) + \( \frac{x^3}{27} \) + ...

r = \( \frac{x}{3} \)

-1 < \( \frac{x}{3} \) < 1

-3 < x < 3

c) 2 + 4x + 8x² + 16x³ + ... 

r = 2x

-1 < 2x < 1

-\( \frac{1}{2} \) < x < \( \frac{1}{2} \)

12.