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