User blog:PhotonicSymmetry/Math Magic

Adding Consecutive Integers:

1 + 2 = 3

4 + 5 + 6 = 7 + 8

9 + 10 + 11 + 12 = 13 + 14 + 15

16 + 17 + 18 + 19 + 20 = 21 + 22 + 23 + 24

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Now, look at the first numbers in each row: Perfect Squares! This series goes on infinitely and can be proven with an algebraic equation.

What if we add consecutive odd numbers?

1 = 1

3 + 5 = 8

7 + 9 + 11 = 27

13 + 15 + 17 + 19 = 64

21 + 23 + 25 + 27 + 29 = 125

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Perfect cubes! But that's not all - look at the median number in the odd rows: perfect squares! You can also find the median of the even rows and see that the are also perfect squares. The squared number is equal to the cubed number in the same equation The amount of numbers in the equation is equivalent to the cube root of the cube.