SME
Discrete Mathematics · Problem type
The steps of a proof by induction
Use this for “Prove that 1 + 2 + … + n = n(n + 1) ÷ 2 for every n ≥ 1.”
Put in order
Put the parts of the proof in order.
1
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2
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3
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4
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5
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Assumptions
•
Induction proves a claim P(n) for every whole number n from a starting value n₀ on.
•
The base case starts the chain; the inductive step shows each case carries over to the next.
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The assumption P(k) is the inductive hypothesis, and the inductive step must use it.
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