Binomial coefficient summatory and Fibonacci numbers questionby olmoelisa Tags: binomial, coefficient, fibonacci, numbers, summatory 

#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 


Register to reply 
Related Discussions  
Binomial coefficient question  Calculus & Beyond Homework  1  
Lucas Numbers/ Fibonacci Numbers Proof  Calculus & Beyond Homework  3  
Where Fibonacci numbers surpass prime numbers  Linear & Abstract Algebra  4  
A quick question on coefficient of binomial expansion  Linear & Abstract Algebra  7 