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Explain what is wrong with the student's "proof" - AQA - A-Level Maths Pure - Question 7 - 2017 - Paper 2
Question 7
Explain what is wrong with the student's "proof". A student notices that when he adds two consecutive odd numbers together the answer always seems to be the differe... show full transcript
Worked Solution & Example Answer:Explain what is wrong with the student's "proof" - AQA - A-Level Maths Pure - Question 7 - 2017 - Paper 2
Step 1
Incorrect Relying on Specific Cases
Answer
The student's proof only checks specific examples (3 + 5, 5 + 7, and 7 + 9) and claims that since these cases work, it must be true for all consecutive odd numbers. This is a common logical fallacy known as 'cherry-picking,' where one cannot generalize a conclusion based solely on limited examples.
Step 2
Failure to Generalize Algebraically
Answer
The proof does not provide an algebraic justification for why the sum of two consecutive odd numbers is always the difference of two square numbers. A true proof should demonstrate the conclusion for all integers, not just a select few. Without a general case set up algebraically, the proof lacks rigor.