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

1. (a) \(S_\infty=\frac{3}{5}\) (0.6)
2. (b) \(S_\infty=18\)

1. (a) \(-8<x<-6\)
2. (b) \(-6<x<6\)
3. (c) \(-1.25<x<1.25\)

1. (a) \(-0.408<x<0.408\)
2. (b) \(x<-3 \text{ or } x>3\)

\(r=0.6\)

\(u_1=75\); terms 75, −18.8, 4.69

1. (a) First three terms: \(6\), \(\frac{12}{5}\), \(\frac{24}{25}\)
2. (b) \(S_\infty=10\)

1. (a) \(r=\frac{1}{3}\) or \(r=\frac{2}{3}\)
2. (b) \(u_1=18\) or \(u_1=9\)

1. (a) \(-7<x<3\)
2. (b) \(S_\infty=\frac{30}{3-x}\)
3. (c) \(S_\infty=15\)

\(x=2\)

\(r=0.7\)

54 thousand

1. (a) \(r=-\frac{1}{5}\) (the other root, \(\frac{6}{5}\), is rejected)
2. (b) \(u_1=30\)