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Binomial coefficient summatory and Fibonacci numbers question 
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#1
Nov2211, 09:05 AM

P: 1

There is a summatory of binomial coefficients wich gives the Fibonacci
numbers: (5 0) + (4 1) + (3 2) = 1 + 4 + 3 = 8 (Fib 7) (9 0) + (8 1) + (7 2) + (6 3) + (5 4) = 1 + 8 + 21 + 20 + 5 = 55 (Fib 10) If I alterne sum and subtraction I obtain 0, 1 or 1: 1  4 + 3 = 0 1  8 + 21  20 + 5 = 1 But what happen if I sum the 1st half and subtract the 2nd half of the sequence? That is: 1 + 4 3 = 2 (or 1  4 3 =  6) 1 + 8 + 21  20  5 = 5 (or 1 + 8  21  20  5 = 37) Any idea/paper/hint? Thank you very much Sandra 


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