### Home > CALC > Chapter 9 > Lesson 9.3.2 > Problem9-99

9-99.

Consider the infinite series below. For each, decide if it converges or diverges and justify your conclusion. If the series converges, find its sum.

For an infinite geometric series:

1. $4 + 4 + 4 + 4 + ...$

This is a geometric series with $r = 1$.

1. $\frac { 1 } { 10 } + \frac { 1 } { 100 } + \frac { 1 } { 1000 } + \ldots$

This is a geometric series with $r = 1/10$.

1. $10 + 9 + 8 + 7 + ...$

This is an arithmetic series. Does an infinite arithmetic series have a finite sum?

1. $- 2 + \frac { 6 } { 5 } - \frac { 18 } { 25 } + \frac { 54 } { 125 } - \dots$

This is a geometric series with $r =-3/5$.