Okay, maybe it was easier than I thought to simplify, I think I figured it out. I just wasn't sure if I should distribute first or FOIL first. And what I ended up with was this:

And it seems like you can divide, which seems weird, but it comes out with the right answer.

So, it seems that I can divide like that, and I simplified correctly?

Awesome! Again thanks for your help! And I will definitely do what you suggested, I plan on devoting a lot of my time to math from here on so I'll probably be here often.

Thanks again!

hi therussequilibrium

Finally remembered that formula and another way to prove it.

You can use a similar method for any summation of the form

Let's say you have spotted that the formula you  want is

Start with the next highest power of n, ie.  n cubed.

Write out this expression for n=1, n=2, n=3, ...n=n

...............    ............    ..............      .............        ............. 

__________________________________________________________________

Now add up each column.  Most of the cube terms on the LHS cancel with most of those on the RHS.  1+1+1...+1 comes to n.

The formula for the {triangle numbers}  is

so

Re-arranging

multiply by 2 to remove the fraction and factorising out the common factor of (n+1)

and so, finally

Bob