## Calculus with Applications (10th Edition)

$$40$$
\eqalign{ & 20 + 10 + 5 + \frac{5}{2} + \cdots \cr & {\text{Sum of a Geometric Series }}\left( {{\text{see page 635}}} \right) \cr & {\text{The infinite geometric series}} \cr & a + ar + a{r^2} + a{r^3} + \cdots \cr & {\text{converges}}{\text{, if }}r{\text{ is in }}\left( { - 1,1} \right),{\text{ to the sum }}\frac{a}{{1 - r}}.{\text{ And diverges if }}r{\text{ is not in }}\left( { - 1,1} \right) \cr & {\text{then this is a geometric series}}{\text{, with }}a = {a_1} = 20 \cr & r = \frac{{10}}{{20}} = \frac{1}{2} \cr & {\text{Since }}r{\text{ is in the interval }}\left( { - 1,1} \right),{\text{ the series converges and has a sum }}\frac{a}{{1 - r}} \cr & \frac{a}{{1 - r}} = \frac{{20}}{{1 - 1/2}} \cr & {\text{simplifying}} \cr & \frac{a}{{1 - r}} = 40 \cr}