Question

What is the sum of this infinite geometric series

Answer 1

You probably know that for $|r|$, we have

$\displaystyle\sum_{i=0}^\infty ar^i=\dfrac a{1-r}$

Your sum starts at $i=1$, so it's equivalent to

$\displaystyle\sum_{i=1}^\infty 12\left(\dfrac12\right)^i=\sum_{i=0}^\infty 12\left(\dfrac12\right)^i-12\left(\dfrac12\right)^0=\dfrac{12}{1-\frac12}-12=12$

so the answer is A.