  ### Home > CALC > Chapter 10 > Lesson 10.1.1 > Problem10-2

10-2.

Examine the different infinite series presented below. Your goal is to decide which series converge (have a finite sum). Rewrite each series using sigma notation. As you work through each example, try to figure out what feature of the series is most critical in its convergence or divergence.

1. $1 + \frac { 3 } { 2 } + \frac { 9 } { 4 } + \frac { 27 } { 8 } + \ldots$

1. $\frac { 1 } { 2 } + \frac { 1 } { 5 } + \frac { 1 } { 10 } + \frac { 1 } { 17 } + \frac { 1 } { 26 } + \ldots$

1. $1 - 2 + 3 - 4 + . ..$

1. $\frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 1 } { 12 } + \frac { 1 } { 20 } + \ldots$

1. $- 2 + 1 - \frac { 2 } { 3 } + \frac { 1 } { 2 } - \frac { 2 } { 5 } + \frac { 1 } { 3 } \dots$

1. $\operatorname { ln } \frac { 1 } { 2 } + \operatorname { ln } \frac { 2 } { 3 } + \operatorname { ln } \frac { 3 } { 4 } + \dots$

1. $100 - 90 + 81 - 72.9 + \ldots$

1. $1 + \frac { 1 } { 8 } + \frac { 1 } { 27 } + \frac { 1 } { 64 } + \ldots$

1. $1 + \frac { 1 } { 2 } + \frac { 1 } { 6 } + \frac { 1 } { 24 } + \frac { 1 } { 120 } + \ldots$

1. $\frac { 1 } { 2 } + 1 + \frac { 9 } { 8 } + 1 + \frac { 25 } { 32 } + \frac { 36 } { 64 } + \ldots$

1. $\frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 4 } + \frac { 4 } { 5 } + \frac { 5 } { 6 } \dots$

1. $1 + \frac { 1 } { \sqrt { 2 } } + \frac { 1 } { \sqrt { 3 } } + \frac { 1 } { 2 } + \frac { 1 } { \sqrt { 5 } } + \ldots$