IB DP Maths: AA HL复习笔记1.5.1 Proof by Induction
What is proof by induction?
- Proof by induction is a way of proving a result is true for a set of integers by showing that if it is true for one integer then it is true for the next integer
- It can be thought of as dominoes:
- All dominoes will fall down if:
- The first domino falls down
- Each domino falling down causes the next domino to fall down
- All dominoes will fall down if:
What are the steps for proof by induction?
- STEP 4: The conclusion step
- State the result is true
- Explain in words why the result is true
- It must include:
- If true for n = k then it is true for n = k + 1
- Since true for n = 1 the statement is true for all n ∈ ℤ, n ≥ 1 by mathematical induction
- The sentence will be the same for each proof just change the base case from n = 1 if necessary
What type of statements might I be asked to prove by induction?
Exam Tip
- Learn the steps for proof by induction and make sure you can use the method for a number of different types of questions before going into the exam
- The trick to answering these questions well is practicing the pattern of using each step regularly
Worked Example
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