Which expression represents an odd number in algebra?

To determine which expression represents an odd number, it is important to understand the characteristics of odd integers in algebra. An odd integer can be expressed in the form of "2k + 1," where k is any integer. This formula reflects the fact that odd numbers are always one more than an even number, which can be expressed as "2k."

The expression "2n + 1" fits this form perfectly, where n is an integer. This means that when you double any integer n (creating an even number, 2n) and then add 1, you are guaranteed to get an odd number.

In contrast, the other expressions do not satisfy the requirements for representing an odd number:

• The expression "2n" represents even numbers because it is simply the multiplication of 2 and any integer n.
• The expression "2n - 1" can generate odd numbers when n is any integer, but it specifically produces a value that is one less than an even number, confirming that it can also yield odd integers depending on the value of n.
• The expression "n² + 1" does not consistently produce odd results, as the square of an even integer will be even, and adding 1