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AS 1 Pure Mathematics

Quick questions on Mathematical induction: the principle and proofs for series, divisibility and recurrence - CCEA A-Level Further Maths

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is not using the assumption?
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The inductive step must visibly use the n=kn = k case; if your k+1k + 1 working never refers to the hypothesis, you have not done induction.
What is a vague conclusion?
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Marks are awarded for the closing sentence. Write "true for n=1n = 1, and if true for n=kn = k then true for n=k+1n = k + 1, hence true for all positive integers nn by induction."
What is q1?
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State the three parts of a proof by induction. [2 marks]
What is q2?
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In proving a sum formula, what do you add to the assumed sum in the inductive step? [1 mark]
What is q3?
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To prove 4n−14^n - 1 is divisible by 33, what is the base case value at n=1n = 1? [1 mark]

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