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I found a relationship between square numbers

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Makes sense
No 17%  17%  [ 1 ]
Yes 83%  83%  [ 5 ]
Total votes : 6

Timdil
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22 Mar 2018, 1:16 am

(n+1)^2 - n^2 = 2n+1

If n = 1 then 2^2 - 1^2 = 3

This means you can write 11^2 as n=0 to 10 2n+1 in sigma notation



Yokokurama
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22 Mar 2018, 1:21 am

I love math but I'm not very skilled at it, you lost me at the second step



Kiprobalhato
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22 Mar 2018, 1:29 am

^ you are wiser than i. i tapped out at the first line.


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Yokokurama
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22 Mar 2018, 1:39 am

Kiprobalhato wrote:
^ you are wiser than i. i tapped out at the first line.

to be honest I had to sort of write it down, I can't do the FOIL method for factoring in my head. Math is painful



naturalplastic
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23 Mar 2018, 1:37 pm

Dang!

You demonstrated that it works for N=1

I tried it with 2, and with 5, and it works.

Three outa three. So that strongly implies that your equation works for all integers. If you really did stumble upon this on your own then its indeed pretty cool. Euclid would be impressed.

++++

Just now tried it with both positive three, and with negative three. Both held true.
So it seems to work with both negative, and with positive numbers.



naturalplastic
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23 Mar 2018, 1:43 pm

Yokokurama wrote:
I love math but I'm not very skilled at it, you lost me at the second step


The equation on the second line is not a "step". It's an example of the equation on the first line. Using the number one as a value for N.



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23 Mar 2018, 4:26 pm

It makes all the sense in the world, and if you’re playing with that at thirteen, I take my hat off :salut:

If you want to check your result, you can work in reverse by finding a succinct expression for the sum of all natural numbers n from 0 to N, both included (though it’s not like it matters if you exclude 0 :P), and then using that to compute your sum of 2 n + 1. It’s what Gauss did, as the legend has it, when his teacher tried to keep the class busy for a while by making them add up 1 + 2 + ⋯ + 100.


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naturalplastic
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23 Mar 2018, 10:03 pm

naturalplastic wrote:
Yokokurama wrote:
I love math but I'm not very skilled at it, you lost me at the second step


The equation on the second line is not a "step". It's an example of the equation on the first line. Using the number one as a value for N.


Never mind

Just realized that you probably meant that thing he said about the "sigma notation". THAT thing is...over my head too. Lol!



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24 Mar 2018, 11:55 pm

Unicode to the rescue!

Code:
 N
⎲
⎳ (2 n + 1) = (N + 1)²
n=0


Image


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25 Mar 2018, 12:02 am

Timdil wrote:
(n+1)^2 - n^2 = 2n+1

If n = 1 then 2^2 - 1^2 = 3

This means you can write 11^2 as n=0 to 10 2n+1 in sigma notation



If I understand it, you are claiming that sum(2n+1) from n=0 to n=10 is equal to 11^2

That is true. They are equivalent representations. Good work. Keep exploring mathematics. There are still many things to be discovered.



DarthMetaKnight
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25 Mar 2018, 1:15 pm

It would be more helpful to society if we found relationships between square people.


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LaetiBlabla
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25 Mar 2018, 4:10 pm

You made me feel like drawing :
https://ibb.co/id8n9n