Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises - Page 605: 31

$a_1 = 9$ $a_2 = 99$ $a_3 = 999$ $a_4 = 9999$ Diverges. The terms increase without a bound as $n$ increases.

$a_n = 10^n - 1$ $a_1 = 10^1 - 1 = 9$ $a_2 = 10^2 - 1 = 99$ $a_3 = 10^3 - 1 = 999$ $a_4 = 10^4 -1 = 9999$ It diverges because the terms increase without a bound as $n$ increases.