OK: so, I found that the hexagonal number for nth term is:

Proof:

(Eventually, I will want to get to

SO:

Let P(n) be the statement .

(Base case) Since , which equals , P(1) is true.

Let k be a pos. integer.

So

Therefore,

=

=

Did i do something wrong? I have an extra +2 in the mix.

Please work with what I have, if possible, I kinda need to use the Strong Induction.