Infinite series: the range of x, r and the first term Problem set A Answers

1. (a) \(S_\infty=\frac{1}{2}\) (0.5)
2. (b) \(S_\infty=\frac{96}{7}\) (13.7)

1. (a) \(5<x<7\)
2. (b) \(-4<x<4\)
3. (c) \(-0.6<x<0.6\)

1. (a) \(-0.447<x<0.447\)
2. (b) \(x<-2 \text{ or } x>2\)

\(r=0.625\)

\(u_1=49\); terms 49, −19.6, 7.84

1. (a) First three terms: \(4\), \(\frac{4}{3}\), \(\frac{4}{9}\)
2. (b) \(S_\infty=6\)

1. (a) \(r=\frac{1}{5}\) or \(r=\frac{4}{5}\)
2. (b) \(u_1=40\) or \(u_1=10\)

1. (a) \(-2<x<4\)
2. (b) \(S_\infty=\frac{12}{4-x}\)
3. (c) \(S_\infty=6\)

\(x=1.5\)

\(r=0.76\)

18 thousand

1. (a) \(r=-\frac{1}{4}\) (the other root, \(\frac{5}{4}\), is rejected)
2. (b) \(u_1=20\)