the fibonacci series

i came across the fibonacci series a year or two ago & remembered it again only now.  it gave me a considerable itch in the ___.   

Starting with 0 and 1, each new number in the series is simply the sum of the two before it.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .

Baffling!  Interesting!  Now how would you explain that?

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