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13 posts

Geek
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Topic # 94728 17-Dec-2011 13:22
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Have been (mildly) pondering this, and I have to say I find it quite interesting and puzzling!
Here it is:
If you add odd numbers in chronological sequence you get a list of square numbers 
So if you go --> 1 + 3 (= 4) + 5 (= 9) + 7 (= 16) + 9 (= 25)..

 

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532 posts

Ultimate Geek
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  Reply # 558974 17-Dec-2011 13:58
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To add to your pondering you will also find that not only do you get squares as you show but that each of those squares is the sum of all the preceding odd numbers.

269 posts

Ultimate Geek
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  Reply # 558975 17-Dec-2011 13:59
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Where is the puzzling bit?

sum{i = 1..n} (2*i - 1) = (2 * sum i) - (sum 1) = (2 * (n * (n+1) / 2)) - (n) = (n^2 + n) - (n) = n^2

Please excuse my liberalism with notation here.

---JvdL---

 
 
 
 


532 posts

Ultimate Geek
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  Reply # 558979 17-Dec-2011 14:08
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Fermat's last theorum is next for you Jarno. Wink



13 posts

Geek
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  Reply # 558988 17-Dec-2011 14:39
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@john, haha yes, well that's how it's supposed to work, as you add consecutive numbers together, to get the square in the first place.
@jorno is this for real?? far over my head 

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