What this exponential inequality proof question tests
This is an easy puzzle that asks you to prove a fundamental inequality comparing exponential and polynomial growth. It's the kind of question used to assess whether a candidate can construct a clear, logical argument and choose an appropriate proof technique.
The core skill being tested is recognizing when an inequality holds for all integers above a threshold, and selecting the right method to establish it. Candidates often consider induction, direct calculation, or algebraic manipulation. The question rewards clean reasoning and the ability to verify a base case before generalizing.
- Mathematical induction
- Base case verification
- Growth rates and asymptotic behaviour
- Algebraic inequality manipulation