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InterviewSolution
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Prove that the sum of two consecutive odd numbers is divisible by 4 |
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Answer» Proof An even number is divisible by 2, so it can be represented by 2n, where n is an integer. If we add 1 to an even number, then it will be odd. Therefore, an odd number can be represented as 2n + 1. If 2n + 1 is an odd number, then the next odd number is 2n + 3 (Why?). Therefore, the sum of two consecutive odd numbers can be represented by (2n + 1) + (2n + 3) = 4n + 4. Factoring, we have 4(n + 1). This means that 4 is a factor of 4n + 4. This means that 4n + 4 is divisible by 4. This implies that the sum of two consecutive odd numbers is divisible by 4. Thx |
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