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Re: Here's a little challenge for you guys.
Posted:
Oct 8, 2013 8:25 AM


Hi Guy,
> Get this: every odd number that is added up to equal > a certain number that is squared will hold true. > > Here it is written out: > _________________________ > > +1 +3 +5 +7 +9 +11 > > 1 4 9 16 25 36 > > 1^2 2^2 3^2 4^2 5^2 6^2 > _________________________ You asked: > Now, I want to know why these values equal the same > numbers (i.e. 9 = 1+3+5 = 3^2, 36 = 1+3+5+7+9+11 = > 6^2)
For a proof without words try writing the numbers in a square array as: 13579 33579 55579 77779 99999 Taking the squares from the top left you can see that 1=1^2, 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2, etc.
Regards, Peter Scales.



