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#51 2012-12-21 23:21:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

Re: Creating Functions?

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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#52 2012-12-21 23:40:10

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

Re: Creating Functions?

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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#53 2012-12-21 23:42:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

Re: Creating Functions?

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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#54 2012-12-21 23:44:55

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

Re: Creating Functions?

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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#55 2012-12-21 23:46:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,366

Re: Creating Functions?

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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#56 2012-12-26 03:31:31

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,380

Re: Creating Functions?

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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