Answer
$$\sum_{k=0}^\infty \left(\frac{1}{4} \right)^k=\frac{4}{3} $$
Work Step by Step
To determine what an infinite geometric series converges to we use the following formula:
$$\sum_{k=0}^\infty ar^k=\frac{a}{1-r} $$
so we must identify $a$ and $r$ for our series $$\sum_{k=0}^\infty \left(\frac{1}{4} \right)^k $$
$a=1$ and $r=\frac{1}{4}$
we plug this into above formula:
$$\sum_{k=0}^\infty \left(\frac{1}{4} \right)^k=\frac{1}{1-\frac{1}{4}}=\frac{4}{3} $$
