We demonstrate that the Collatz conjecture generates cycles that consistently converge to the series defined by (4n - 2), ultimately terminating at the number 2. We propose an innovative algorithm that predicts the positions within this series during each cycle. Through a rigorously defined metric, we establish that these positions invariably converge to position 1, corresponding to the number 2 in the Collatz sequence (2 to 1 to 4 to 2). This approach not only confirms the validity of the conjecture for all positive integers but also provides a novel framework for understanding its cyclic behavior.