Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises - Page 605: 40

$a_1 = -1$ $a_2 = -11$ $a_3 = -111$ $a_4 = -1111$ Diverges. The terms are decreasing without a bound.

$a_{n+1} = 10a_n -1$; $a_0 = 0$ $a_1 = 10(a_0)-1 = -1$ $a_2 = 10(a_1)-1 = -11$ $a_3 = 10(a_2)-1 = -111$ $a_4 = 10(a_3)-1 = -1111$ Diverges. The terms are decreasing without a bound.