Understanding Proof by Induction

Understanding Proof by Induction

Assessment

Interactive Video

Created by

Aiden Montgomery

Mathematics

9th - 12th Grade

Hard

06:35

10 questions

Show answers

1.

Multiple Choice

30 sec

1 pt

What is the primary purpose of mathematical induction?

To find the roots of a polynomial

To prove that a mathematical statement is always true

To calculate integrals

To solve complex equations

2.

Multiple Choice

30 sec

1 pt

In a proof by induction, what is the base case?

A hypothetical scenario

A step where the statement is assumed false

The final step of the proof

The initial step where the statement is assumed true for the first value

3.

Multiple Choice

30 sec

1 pt

What does the inductive case in a proof by induction involve?

Proving the statement for a specific number

Calculating the derivative

Finding a counterexample

Assuming the statement is true for n and proving it for n+1

4.

Multiple Choice

30 sec

1 pt

How does the domino analogy explain the principle of induction?

Pushing the first domino ensures all others fall, similar to proving the base case and inductive step

Each domino represents a different mathematical operation

Dominoes are irrelevant to induction

Dominoes are used to calculate probabilities

5.

Multiple Choice

30 sec

1 pt

What is the statement being proved in the example of a proof by induction?

2^n = n^2

n^2 + n + 1 = 0

1 + 3 + 5 + ... + (2n-1) = n^2

1 + 2 + 3 + ... + n = n(n+1)/2

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