Variation 3 · answer guide
Mathematical induction — Check n=2 numerically
Question
Verify the 2023 identity numerically for and .
This practice question was inspired by Question 12(b) in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.
Step by step
- Set up the solution: show the base case, state the assumption for n=k, and transform the k+1 case using that assumption.: LHS ; RHS .
- State the final answer clearly in the form the question requested.: LHS ; RHS .
Common mistake: changing so many features that the new example no longer tests the same mathematical idea.
Verification: Spot-check before writing the formal induction.
Any mark labels are a TestMum study aid, not an official NESA marking allocation.
← Back to 2023 HSC Extension 1 paper Question 12(b)