Final answer:
The product of multiplying -1 by itself an odd number of times (2m + 1) will be negative, thus the answer is -1. Therefore, the correct option is b).
Step-by-step explanation:
The question inquires about the product of multiplying the number -1 by itself an odd number of times, specifically 2m + 1 times, where m is a natural number. To understand the result, one must consider the rules of multiplication involving negative numbers. When two negative numbers are multiplied together, the result is positive. However, when multiplying an odd number of negative numbers, the result will be negative since there is an unmatched negative number in the product.
Therefore, the sequence (-1) x (-1) x (-1) × ... (2m + 1) times will result in a negative product. This is because there will always be an extra -1 after pairing up -1s. Thus, the correct answer is (b) – 1. In conclusion, when m is a natural number and -1 is multiplied by itself 2m + 1 times, the product is -1. So, we should mention the correct option in the final part, which is -1.