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# 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:

$$1={ 1 }^{ 2 }$$
$$1+2+1={ 2 }^{ 2 }$$

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

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

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

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

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

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

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

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
2 years, 9 months ago

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Thank you for your help! · 2 years, 9 months ago

Oh, thank you. I am just a newbie here! · 2 years, 9 months ago

Looks great! You are a fast learner. Staff · 2 years, 9 months ago

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. Staff · 2 years, 9 months ago