Which of the following is a valid expression for the sum of the first n odd numbers?

The sum of the first n odd numbers is indeed represented by n^2. This result can be established through mathematical induction or by observing patterns in the sums of the first few odd numbers.

When adding the first few odd numbers:

• The first odd number is 1.

• The sum of the first two odd numbers (1 + 3) is 4, which is 2^2.

• The sum of the first three odd numbers (1 + 3 + 5) is 9, which is 3^2.

• The sum of the first four odd numbers (1 + 3 + 5 + 7) is 16, which is 4^2.

This pattern suggests that as you continue adding more odd numbers, the total equals the square of how many numbers you’ve added, confirming that the sum of the first n odd numbers is n^2. This relationship is a fundamental concept in algebra and number theory, illustrating how sequences can behave under summation operations.

In contrast, the other expressions do not accurately describe the sum of the first n odd numbers:

• n simply counts how many odd numbers there are and does not correspond to their sum.

• n(n + 1)