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)

Proof:

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.

QED