LCHL Induction
Your progress through this topic0 of 7 lessons
Lessons in this topic
All 7 lessons, in order — each one ticks off as you open it.
1Introduction2Inequalities3Factorials4Divisibility5Series6Proof of De Moivre’s Theorem by induction7Induction 7 Proof by induction of the Sum of a geometric series
✍️ Learning work — the four-step method
Learn this skeleton off — exam answers lose marks without it.
1Prove P(n) is true for n = (the first value)
2Assume P(n) is true for n = k
3Hence, prove P(n) is true for n = k + 1
4State the conclusion
The four types of induction
Series (summation)Prove a sum formula — append the (k+1)th term, then factor.DivisibilityProve aⁿ ± c is divisible by D — substitute and factor.InequalitiesProve e.g. 3ⁿ > 2n — split into pairs with the coefficient.FactorialsProve factorial-based statements — the same four-step skeleton.
A rule you must know
★ Must learn
Check it against the exam
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