Candidates should be able to:
- use the method of mathematical induction to establish a given result (e.g. n∑r=1r4=14n2(n+1)2,un=12(1+3n−1) for the sequence given by un+1=3un–1 and u1=1,(4−16−1)n=(3×2n−21−2n3×2n+1–63–2n+1),32n+2×5n–3 is divisible by 8.);
- recognise situations where conjecture based on a limited trial followed by inductive proof is a useful strategy, and carry this out in simple cases. (e.g. find the nth derivative of xex, find n∑r=1r×r!.
Proof by induction – Further Pure Maths 1 Video (1:36:40)
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