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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,678

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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: 90,678

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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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: 90,678

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 agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,532

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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