Question #N888
What is the value of $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...$ ?
A. 1
B. 2
C. $\frac{3}{2}$
D. $\frac{5}{2}$
Correct Answer is: A
This is an infinite geometric series. The first term is $\frac{1}{2}$ and the common ratio is $\frac{1}{2}$. The sum of an infinite geometric series is given by $\frac{a}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Therefore, the sum of this series is $\frac{\frac{1}{2}}{1 - \frac{1}{2}} = \frac{\frac{1}{2}}{\frac{1}{2}} = 1$.