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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,449

Hi;

Okay, I am glad to help.

About catching up, I recommend you post your questions here when you get stuck. There are knowledgeable people here.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**therussequilibrium****Member**- Registered: 2012-12-21
- Posts: 36

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?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,449

Hi;

That is correct. Do not forget to add them up to make the formula.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**therussequilibrium****Member**- Registered: 2012-12-21
- Posts: 36

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!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,449

Hi;

You are welcome. Have a good holiday.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,383

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

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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