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.
# 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))
Consider Fibonacci number F(N), where N is a positive integer, defined as follows. F(1) = 1...
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