Proof by induction Quiz
10 questions · easy to harder · Discrete Math · score and step-by-step answers
How it works
- 10 questions, about 30 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 0 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise the lesson with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
1 Question 1
Prove 1 + 2 + ... + n = n(n + 1)/2 by inductionType the answer.
2 Question 2
Prove 2 + 4 + 6 + ... + 2n = n(n + 1) by inductionType the answer.
3 Question 3
Prove 3 + 6 + 9 + ... + 3n = 3n(n + 1)/2 by inductionType the answer.
4 Question 4
Prove 1 + 2 + 4 + ... + 2n − 1 = 2n − 1 by inductionType the answer.
5 Question 5
Prove 2 + 5 + 8 + ... + (3n − 1) = n(3n + 1)/2 by inductionType the answer.
6 Question 6
Prove 4 + 8 + ... + 4n = 2n(n + 1) by inductionType the answer.
7 Question 7
Prove 2 + 6 + 18 + ... + 2 × 3n − 1 = 3n − 1 by inductionType the answer.
8 Question 8
Prove 12 + 22 + ... + n2 = n(n + 1)(2n + 1)/6 by inductionType the answer.
9 Question 9
Prove 1 + 4 + 16 + ... + 4n − 1 = (4n − 1)/3 by inductionType the answer.
10 Question 10
Prove 2 + 4 + 8 + ... + 2n = 2n + 1 − 2 by inductionType the answer.