I've decided to learn the basics of proofs and here is my first attempt. Could I improve or simplify my proof in any way? Is my formal language correct? Thanks!
Let $n$ be any integer. $n(n+2) = (n+1)^2 - 1$ I will prove this identify by induction.
First, check with $n=1$;
$1 \times 3 = 2^2 + 1 \equiv 3 = 3$
Inductive step: Assume that the identity is true for n = k;
$k(k+2) = (k+1)^2 - 1$
When $n = k + 1$;
$(k+1)((k+1)+2) = ((k+1)+1)^2 - 1$
$\equiv k+1(k+3) = (k+2)^2 - 1$
Let $n = k + 1$;
$n(n+2) = (n+1)^2 - 1$
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