I'm about to leave now, so i'll post a solution. if you want to keep trying, you don't have to look at it. here goes.
We wish to show that the sum of the first n positive, even integers is n(n + 1)
We proceed by induction.
Let " " for all
Then is true, since
Now assume is true, for some integer . We show that is true.
Since is true, we have
adding the next even integer to both sides, we obtain:
which is precisely the statement
Thus, holds by induction.