Show that the sum of two consecutiv odd numbers is an even number.

To show that the sum of two consecutive odd numbers is an even number, we can follow these steps: 1. **Define the odd numbers**: Let the first odd number be represented as \( n \). Since odd numbers can be expressed in the form of \( 2k + 1 \) (where \( k \) is an integer), we can write: - First odd number: \( n = 2k + 1 \) - Second consecutive odd number: \( n + 2 = 2k + 3 \) 2. **Calculate the sum**: Now, we will find the sum of these two consecutive odd numbers: \[ \text{Sum} = n + (n + 2) = (2k + 1) + (2k + 3) \] 3. **Simplify the expression**: Simplifying the sum gives: \[ \text{Sum} = 2k + 1 + 2k + 3 = 4k + 4 \] 4. **Factor the result**: We can factor out a 4 from the expression: \[ \text{Sum} = 4(k + 1) \] 5. **Conclusion**: Since \( 4(k + 1) \) is clearly a multiple of 4, it is also an even number (as any multiple of 2 is even). Therefore, we have shown that the sum of two consecutive odd numbers is an even number. Thus, the statement is proven.