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#51 2012-12-22 22:21:42

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#52 2012-12-22 22:40:10

therussequilibrium
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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?

#53 2012-12-22 22:42:10

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#54 2012-12-22 22:44:55

therussequilibrium
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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!

#55 2012-12-22 22:46:58

bobbym
Administrator

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Re: Creating Functions?

Hi;

You are welcome. Have a good holiday.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#56 2012-12-27 02:31:31

bob bundy
Moderator

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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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