An alternating series, such as $100 – 80 + 64 – 51.2 + …$, has terms that alternate in sign ($+$ and $–$).

1. What is the common ratio for $100 – 80 + 64 – 51.2 + …$?

   Step (a):

   $r=\frac{-80}{100}\text{ or }\frac{64}{-80}$

2. Calculate the sum of this infinite series.

   Hint:

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