Proof by induction Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/discrete-math/proof-by-induction/quiz/

1. 1

   Prove 1 + 2 + ... + n = n(n + 1)/2 by induction

   Answer: ____________________

2. 2

   Prove 2 + 4 + 6 + ... + 2n = n(n + 1) by induction

   Answer: ____________________

3. 3

   Prove 3 + 6 + 9 + ... + 3n = 3n(n + 1)/2 by induction

   Answer: ____________________

4. 4

   Prove 1 + 2 + 4 + ... + 2^{n − 1} = 2ⁿ − 1 by induction

   Answer: ____________________

5. 5

   Prove 2 + 5 + 8 + ... + (3n − 1) = n(3n + 1)/2 by induction

   Answer: ____________________

6. 6

   Prove 4 + 8 + ... + 4n = 2n(n + 1) by induction

   Answer: ____________________

7. 7

   Prove 2 + 6 + 18 + ... + 2 × 3^{n − 1} = 3ⁿ − 1 by induction

   Answer: ____________________

8. 8

   Prove 1² + 2² + ... + n² = n(n + 1)(2n + 1)/6 by induction

   Answer: ____________________

9. 9

   Prove 1 + 4 + 16 + ... + 4^{n − 1} = (4ⁿ − 1)/3 by induction

   Answer: ____________________

10. 10

    Prove 2 + 4 + 8 + ... + 2ⁿ = 2^{n + 1} − 2 by induction

    Answer: ____________________