## Calculus 8th Edition

In this explicit form we see that $r$ =|$0.73|\lt1$ which means that this geometric series will converge. Now, use the formula from definition 4 in page 750 , knowing that $a$ refers to the first term which is $12$ and using the explicit $r$ and we get $S= \frac{a}{1-r}$ = $\frac{12}{1-0.73} = \frac{12}{0.27} = \frac{400}{9}$ Result: the series converges and its sum is $\frac{400}{9}$ .