Prove Fibonacci upper bound using strong induction
Analyze the prove fibonacci upper bound using strong induction.
Examples
Input:"proof_case_1"
Output:true
Input:"proof_case_2"
Output:true
Hints
Recall the definition of strong induction and how it differs from regular induction, focusing on the induction hypothesis.
Identify the base cases for the Fibonacci sequence and verify the upper bound holds for these initial values.
Assume the upper bound holds for all Fibonacci numbers up to \( F_k \) and prove it for \( F_{k+1} \) using the recurrence relation \( F_{k+1} = F_k + F_{k-1} \).
Prove Fibonacci upper bound using strong induction
Analyze the prove fibonacci upper bound using strong induction.