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## btone

13 posts

Geek
Inactive user

Topic # 94728 17-Dec-2011 13:22

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)..

## John2010

532 posts

Ultimate Geek
+1 received by user: 28

Reply # 558974 17-Dec-2011 13:58

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.

## Jarno

269 posts

Ultimate Geek
+1 received by user: 49

Reply # 558975 17-Dec-2011 13:59

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---

## John2010

532 posts

Ultimate Geek
+1 received by user: 28

Reply # 558979 17-Dec-2011 14:08

Fermat's last theorum is next for you Jarno.

## btone

13 posts

Geek
Inactive user

Reply # 558988 17-Dec-2011 14:39

@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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