Answers to quiz 1

1. The series −ln(1−x) = x + x2/2 + x3/3 + x4/4 + ... converges for −1≤x<1 (Eq. 13.4, x⇒−x).

2. (A) 1 + x + x2 + x3 + ...: geometric series (r = x), converges for |x|<1
(B) 1 + x + x2/2 + x3/3 + ... = −ln(1−x), converges for −1≤x<1
(C) 1 + x + x2/2! + x3/3! + ... = exp(x), converges for all x
(D) 1 + x + x2/22 + x3/23 + ...: 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 a0 = 1/2, r = 1/2)

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