Prove this identity relating the Fibonacci numbers and the
Chapter 11, Problem 17E(choose chapter or problem)
Problem 17E
Prove this identity relating the Fibonacci numbers and the binomial coefficients:
fn+1 = C (n,0) + C(n – 1,1) + ...+ C(n – k,k). where n is a positive integer and k =[n/2]. [Hint: Let an = C (n,0) + C(n – 1,1) + ...+ C(n – k,k). Show that the sequence {an} satisfies the same recurrence relation and initial conditions satisfied by the sequence of Fibonacci numbers.]
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