Question

Consider Fibonacci number F(N), where N is a positive integer, defined as follows. F(1) = 1 F(2) = 1 F(N) = F(N-1) + F(N-2) for N > 2

a) Write a recursive function that computes Fibonacci number for a given integer N≥ 1.

b) Prove the following theorem using induction: F(N) < ΦN for integer N≥ 1, where Φ = (1+√5)/2.

Answer 1

# Python program to display the Fibonacci sequence up to n-th term using recursive functions

def recur_fibo(n):
"""Recursive function to
print Fibonacci sequence"""
if n <= 1:
return n
else:
return(recur_fibo(n-1) + recur_fibo(n-2))

# Change this value for a different result
nterms = 10

# uncomment to take input from the user
#nterms = int(input("How many terms? "))

# check if the number of terms is valid
if nterms <= 0:
print("Plese enter a positive integer")
else:
print("Fibonacci sequence:")
for i in range(nterms):
print(recur_fibo(i))