Proof by induction not making sense

Proof by induction not making sense

Proving by induction. We'd like to show that $2 + 4 + 6 + \cdots+ 2n = n(n
+ 1)$.
A nice way to do this is by induction. Let $S(n)$ be the statement above.
An inductive proof would have the following steps: Show that $S(1)$ is
true. Show that if $S(1),\ldots,S(k)$ are true, then so is $S(k + 1)$.



This question is really starting to bug me, am I doing something wrong or
is the equation wrong for that series? It only seems to work for $S(1)$
but after that it does not give the correct series. The $n(n+1)$ series is
$2, 6, 12,\ldots.$ I'm really confused can someone please nudge me in the
right direction (I know how proofs by induction works) I'm just having
problems with this one in particular.