Home > PC3 > Chapter 13 > Lesson 13.1.3 > Problem13-36

13-36.

Calculate the sum of each series, if it exists.

1. $\displaystyle \sum _ { n = 1 } ^ { \infty } \frac { 4 } { 9 } ( 7 ) ^ { n - 1 }$

1. $\displaystyle \sum _ { k = 1 } ^ { 5 } 4 ( \frac { 3 } { 5 } ) ^ { k - 1 }$

1. $\displaystyle \sum _ { j = 1 } ^ { \infty } 9 ( \frac { 7 } { 9 } ) ^ { j }$

These are all geometric series. Two are infinite, one is not.

$S_n=\frac{a(1-r^n)}{1-r}\text{ for }|r|<1$

$S=\frac{a}{1-r}\text{ for }|r|<1$