Prove that the difference between the squares of two consecutive integers is equal to the sum of the two integers.

Question

Prove that the difference between the squares of two consecutive integers is equal to the sum of the two integers.
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Solution 1

Sure, let's prove this step by step.

Let's denote the two consecutive integers as n and n+1.

The square of n is n^2 and the square of n+1 is (n+1)^2.

The difference between the squares of these two consecutive integers is (n+1)^2 - n^2.

We can expand (n+1)^2 to get n^2 + 2n + 1.

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