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← 2021 HSC Extension 1 paper Question 12(c)

Variation 1 · answer guide

Mathematical induction — Base and one step only

Question

Verify the given identity for by direct computation of both sides.

This practice question was inspired by Question 12(c) in the 2021 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

  1. Set up the solution: show the base case, state the assumption for n=k, and transform the k+1 case using that assumption.LHS .
  2. State the final answer clearly in the form the question requested.RHS .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Both sides equal .

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

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