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Mathematical Induction Concepts and Proofs

Mathematical Induction Concepts and Proofs

Assessment

Interactive Video

Mathematics

9th - 12th Grade

Practice Problem

Hard

CCSS
6.EE.A.1, HSA.APR.C.4, HSF-LE.A.1A

+1

Standards-aligned

Created by

Jackson Turner

FREE Resource

Standards-aligned

CCSS.6.EE.A.1
,
CCSS.HSA.APR.C.4
,
CCSS.HSF-LE.A.1A
CCSS.8.EE.A.2
,
The video tutorial explains how to use mathematical induction to prove that n squared is less than 2 to the power of n for all integers n greater than or equal to five. It begins by comparing the growth of n squared and 2^n, showing that the left side grows slower than the right. The base case is verified for n=5, and the inductive step is demonstrated, proving the inequality for n+1. The tutorial concludes by affirming the proof's validity for all n greater than or equal to five.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the main goal of the mathematical induction proof discussed in the video?

To prove that n squared is less than two to the power of n for all integers n less than five.

To prove that n squared is equal to two to the power of n for all integers n.

To prove that n squared is less than two to the power of n for all integers n greater than or equal to five.

To prove that n squared is greater than two to the power of n for all integers n.

Tags

CCSS.8.EE.A.2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does the increase in n affect the expression n squared?

It increases the base of the square to the next square number.

It doubles the value of n squared.

It decreases the value of n squared.

It has no effect on n squared.

Tags

CCSS.6.EE.A.1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the base case used in the proof?

n = 4

n = 5

n = 6

n = 7

Tags

CCSS.6.EE.A.1

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of 5 squared compared to 2 to the power of 5?

5 squared is less than 2 to the power of 5.

5 squared is not comparable to 2 to the power of 5.

5 squared is equal to 2 to the power of 5.

5 squared is greater than 2 to the power of 5.

Tags

CCSS.HSA.APR.C.4

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the inductive step, what assumption is made about P(k)?

P(k) is true.

P(k) is false.

P(k) is irrelevant.

P(k) is undefined.

Tags

CCSS.HSA.APR.C.4

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the expression for the square of (k+1)?

k squared plus k plus 1

k squared plus 2k plus 1

k squared plus 3k plus 1

k squared plus 4k plus 1

Tags

CCSS.HSF-LE.A.1A

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What substitution is made for k squared in the inductive step?

k squared is substituted with 2 to the power of k.

k squared is substituted with 2 to the power of k plus 1.

k squared is substituted with k plus 1.

k squared is substituted with 2k.

Tags

CCSS.HSF-LE.A.1A

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