I just realized that the difference between $n^2$ and $(n+1)^2$ is exactly the $n$th odd number. For example: $5^2 - 4^2 = 9$, the 5th odd number. Is there a proof of this that I can study? This is just my nephew and I playing with series and simple programming problems.
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6$$(n+1)^2=n^2+2n+1$$ subtract $n^2$. – SlipEternal Apr 22 '20 at 01:15
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1Welcome to Mathematics Stack Exchange. Every odd number is the difference of two squares – J. W. Tanner Apr 22 '20 at 01:22
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Mind-blowing, @J.W.Tanner! Thank you both! – Carlos Mascarua Apr 22 '20 at 02:12