**Answers to quiz 1**

1. The series
−ln(1−x) = x + x^{2}/2 + x^{3}/3 + x^{4}/4 + ...
converges for −1≤x<1 (Eq. 13.4, x⇒−x).

2.
(A) 1 + x + x^{2} + x^{3} + ...: geometric series (r = x), converges for |x|<1

(B) 1 + x + x^{2}/2 + x^{3}/3 + ... = −ln(1−x), converges for −1≤x<1

(C) 1 + x + x^{2}/2! + x^{3}/3! + ... = exp(x), converges for all x

(D) 1 + x + x^{2}/2^{2} + x^{3}/2^{3} + ...: geometric series (r = x/2), converges for |x|<2

Answer: (C)

3. 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... = 1 (geometric series with a_{0} = 1/2, r = 1/2)

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