Final answer:
The series follows a halving pattern, meaning each number is half the value of the previous one. By continuing this pattern, the number that follows 1/4 in the series is 1/8, which corresponds to option 2)(1/8).
Step-by-step explanation:
Upon examining the series (2, 1), (1/2), and (1/4), we can determine a pattern where each subsequent number is half the value of the previous one. Starting with 2, we divide by 2 to get 1, divide 1 by 2 to get 1/2 and divide 1/2 by 2 to get 1/4. Following this pattern, the next step is to divide 1/4 by 2 which would yield 1/8. Therefore, the answer to the question, "What number should come next in the series: (2, 1), (1/2), (1/4), ...?" is (1/8).
To clarify further, the series is a simple geometric progression where each term is obtained by multiplying the previous term by 1/2. This halving pattern is a consistent method that can be applied to each term to predict the next one. So, when we apply this pattern to the term (1/4), we obtain the next term (1/8). The mention of the correct option in the final part of your question corresponds with option 2)(1/8), which is the correct answer to what comes next in the given series.