Evaluate the geometric series or state that it diverges.
\[
\sum_{j=1}^{\infty} 4^{-2 j}
\]

Step 1 ：We are given the geometric series \(\sum_{j=1}^{\infty} 4^{-2 j}\).

Step 2 ：This is a geometric series with common ratio \(r = 4^{-2} = \frac{1}{16}\).

Step 3 ：The sum of an infinite geometric series is given by the formula \(\frac{a}{1-r}\), where \(a\) is the first term of the series and \(r\) is the common ratio.

Step 4 ：In this case, \(a = 4^{-2} = \frac{1}{16}\) and \(r = \frac{1}{16}\).

Step 5 ：We can use this formula to find the sum of the series.

Step 6 ：Substituting the values into the formula, we get \(\frac{0.0625}{1-0.0625} = 0.06666666666666667\).

Step 7 ：Final Answer: The sum of the geometric series is \(\boxed{0.06666666666666667}\).