Intermediate
Discrete Mathematics & Math
Q56 / 100
What is a generating function approach to Fibonacci numbers?
Correct! Well done.
Incorrect.
The correct answer is B) F(x) = x/(1-x-x²) is the ordinary GF for Fibonacci; partial fractions yield Binet's formula F(n) = (φⁿ - ψⁿ)/√5
B
Correct Answer
F(x) = x/(1-x-x²) is the ordinary GF for Fibonacci; partial fractions yield Binet's formula F(n) = (φⁿ - ψⁿ)/√5
Explanation
F(x) = Σ F_n x^n = x/(1-x-x²). Partial fraction decomposition gives Binet: F_n = (φⁿ - ψⁿ)/√5 where φ=(1+√5)/2, ψ=(1-√5)/2. GFs provide closed forms for many combinatorial sequences.
Progress
56/100