Step 1 :The given series is a geometric series with common ratio \(r = -\frac{1}{3}\) and first term \(a = 4\).
Step 2 :A geometric series converges if and only if \(|r| < 1\). In this case, \(|r| = \frac{1}{3} < 1\), so the series converges.
Step 3 :The sum of an infinite geometric series is given by the formula \(\frac{a}{1 - r}\).
Step 4 :Substituting the values of \(a\) and \(r\) into the formula, we get the sum as 3.
Step 5 :Final Answer: The series converges. The sum of the series is \(\boxed{3}\).