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MathidiaMathematics Academy
Discrete mathematics
Lesson 3 of 10
Introduction

Proof techniques

Objective. Use direct proof, contradiction and induction.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: 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.

-1012234+2
Number line from -1 to 4 with a jump of 2 forwards from 1
  1. 1Base case n = 1: both sides equal 1.
  2. 2Assume true for k.
  3. 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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