Common Cases of Proof by Induction (Edexcel A-Level Further Mathematics): Quizzes

📚Quizzes
Revision NotesModel AnswersQuizzesFlashcardsExam Questions
Common Cases of Proof by Induction
Sign up to keep practising.Create a free account to play more quizzes and track your progress.

Practise the questions

10 questions from this quiz

Show

How many main types of problems is induction often used to prove?

Three

What is the first step in a proof by induction?

Base case

What is ∑r=1nr2\sum_{r=1}^n r^2 equal to?

n(n+1)(2n+1)6\frac{n(n+1)(2n+1)}{6}

For n=1n=1, what does ∑r=11r2\sum_{r=1}^1 r^2 equal?

11

In the summation example, what is the final factorised form for n=k+1n=k+1?

(k+1)(k+2)(2k+3)6\frac{(k+1)(k+2)(2k+3)}{6}

What is 13+2×11^3 + 2 \times 1 in the divisibility example base case?

33

In the divisibility example, how is the inductive hypothesis expressed?

k3+2k=3mk^3 + 2k = 3m

What is (k+1)3(k+1)^3 expanded to in the divisibility proof?

k3+3k2+3k+1k^3 + 3k^2 + 3k + 1

What is a common mistake in proof by induction?

Not defining inductive hypothesis

For n=1n=1, what is the top-left entry of the matrix result?

33

Explore Edexcel A-Level Further Mathematics Revision Notes by Topics

Proof by Induction

Explore Edexcel A-Level Further Mathematics Model Answers by Topics

Proof by Induction

Explore Edexcel A-Level Further Mathematics Flashcards by Topics

Proof by Induction

Explore Edexcel A-Level Further Mathematics Exam Questions by Topics

Proof by Induction

Join 100,000+ A-Level students studying Quizzes with us.

Select your subjects, and get access to A+ resources today.