Prove that the difference between the squares of any two consecutive integers is equal to the sum of these two integers.
A problem of this nature seems complex at first until you break it down and see what it is really asking you to find. We can represent two consecutive integers as x and x + 1. The problem asks us to prove something. It asks us to show that (x+1)2 - x2 is equal to the sum of x + (x+1) = 2x + 1.
Thanks to our notation, the answer falls into place quite easily. Expanding (x+1)2, as it is an algebraic identity, and solving for the difference between the two squares gives us the desired result.
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