Math induction sum of even numbers I need to prove by induction this thing:
$2+4+6+........+2n = n(n+1)$
so, this thing is composed by sum of pair numbers, so its what I do, but I'm stucked.
$2+4+6+\cdots+2n = n(n+1)$
$(2+4+6+\cdots+2n)+(2n+2) = n(n+1) + (2n+2) $
$n(n+1)+(2n+2) = n(n+1)+(2n+2) $
$n^2 + 3n + 2$
$n(n+2+1)+2$
I don't know how to move forward from this.
Thanks.

$2+4+6+........+2n = n(n+1)$
$2+4+6+........+2n+2(n+1) = n(n+1)+2(n+1)=(n+1)(n+2)$
