Discrete mathematics
Lesson 3 of 10
Proof techniques
Objective. Use direct proof, contradiction and induction.
The key idea
Induction proves a statement for all naturals by establishing a base case and showing each case implies the next.
Worked example
Prove 1 + 2 + … + n = n(n+1)/2.
- 1Base case n = 1: both sides equal 1.
- 2Assume true for k.
- 3Add k+1 to both sides and simplify to (k+1)(k+2)/2.
Answer: True for all n by induction
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