#### Answer

False.

#### Work Step by Step

False. Given the geometric series
$a_1=\frac{1}{2}, r=\frac{1}{2}, a_n=\frac{1}{512}$
we have
$a_n=a_1r^{n-1}$ or $\frac{1}{512}=\frac{1}{2}(\frac{1}{2})^{n-1}=(\frac{1}{2})^n$
Thus, $n=9$ and the sum is
$S_9=\frac{a_1(1-r^9)}{1-r}$
We can calculate, not just estimate, the sum, without precisely knowing the middle values.