### Home > PC3 > Chapter 12 > Lesson 12.1.4 > Problem12-57

12-57.

Calculate the sum of each of the following infinite geometric series. If the sum is “$∞$,” explain why.

$S=\frac{a}{1-r}$

1. $1 +\frac { 1 } { 2 }+\frac { 1 } { 4 }+\frac { 1 } { 8 }\:+\:...$

1. $16 + 4 + 1 +\frac { 1 } { 4 }+\frac { 1 } { 16 }\:+\: ...$

1. $a + 0.9a + 0.81a + 0.729a + …$

$r = 0.9$

1. $1 + 1.1 + 1.21 + 1.331 + …$

What happens when $r > 1$?