Discuss more about: Pyramid Investigations by Arron Kau

After solving all 6 problems, I just remembered a very fast, easy and awesome way to solve other problems like these 6 problems. (Note: You can easily prove my equations!)

Back to our easy equations:

1=12 1={ 1 }^{ 2 }
1+2+1=22 1+2+1={ 2 }^{ 2 }

1+2+3+2+1=32 1+2+3+2+1={ 3 }^{ 2 }
...

And: 1=1 1={ 1 }
1+2=2×(2+1)2 1+2=\frac { 2\times (2+1) }{ 2 }
1+2+3=3×(3+1)2 1+2+3=\frac { 3\times (3+1) }{ 2 }
...

These are very simple right, I think you can prove them easily. But there is a question: Can you calculate quickly this sum: 1+4+7+...+34=? 1 + 4 + 7 + ... + 34 = ?

My answer is: Yes, you can! But how?

Using this sum above First, calculate the total terms of this sum: Numbers of Terms =( The last term - The first term) The difference between each term+1= \frac { ( \text{ The last term - The first term} ) } { \text{ The difference between each term}} +1 .
In this equation, the number of terms is: 34−13+1=12 \frac { 34-1 }{ 3 } +1=12

Our first step is completed, now move to the next step To sum this equation, use this: The sum =(The first term + The last term)×Number of terms 2= \frac {{ ( \text{The first term + The last term}) \times} {\text {Number of terms }}}{2}

So in this equation: The sum is: (34+1)×122=210\frac { (34+1)\times 12 }{ 2 } =210

This is my solution, and you can use it in all arithmetic series. I hope to discuss more with all of you.

Note by Dang Anh Tu
7 years, 2 months ago

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Comments

Note: To use latex, you have to place it within the brackets \ ( code \ ), with spaces removed. Also, you don't need to use \quad to space out text. Just leave them outside of the brackets. If you want to include text, I would suggest using \text{ XXX } instead, as this makes it display as per normal, instead of italicised.

I edited the first few paragraphs of your note, to give you an example. You can edit it to see the changes that I made.

Calvin Lin Staff - 7 years, 2 months ago

Oh, thank you. I am just a newbie here!

Dang Anh Tu - 7 years, 2 months ago

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Looks great! You are a fast learner.

Calvin Lin Staff - 7 years, 2 months ago

Thank you for your help!

Dang Anh Tu - 7 years, 2 months ago
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