Inductive step: Assume that the formula holds for some $k\geq 1$, that is, $2+4+6+\cdots+2k=k(k+1)$. We want to show that it also holds for $k+1$, that is, $2+4+6+\cdots+2(k+1)=(k+1)(k+2)$.
Starting with the left-hand side of the equation for $k+1$, we
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