Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises - Page 605: 51

Diverges

$a_{n+1} = 2a_n + 1$; $a_0 = 0$ $a_0 = 0$ $a_1 = 1$ $a_2 = 3$ $a_3 = 7$ $a_4 = 15$ $a_5 = 31$ $a_6 = 63$ $a_7 = 127$ $a_8 = 255$ $a_9 = 511$ $a_{10}= 1023$ The terms of the sequence are increasing without a bound.