Understanding Proof by Induction

Understanding Proof by Induction

Assessment

Interactive Video

Mathematics

7th - 12th Grade

Practice Problem

Hard

CCSS
HSF.IF.A.2, HSA.SSE.B.4

Standards-aligned

Created by

Olivia Brooks

FREE Resource

Standards-aligned

CCSS.HSF.IF.A.2
,
CCSS.HSA.SSE.B.4
The video tutorial explains the concept of a function S of n, defined as the sum of all positive integers up to and including n. The instructor demonstrates how to prove that this sum can be expressed as n(n+1)/2 using proof by induction. The process involves proving a base case and then showing that if the formula holds for an integer k, it also holds for k+1. This method ensures the formula is valid for all positive integers, illustrating the cascading effect of induction.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the function S of n defined as?

The difference of all positive integers up to n

The sum of all positive integers up to and including n

The product of all positive integers up to n

The division of all positive integers up to n

Tags

CCSS.HSF.IF.A.2

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of S(3)?

9

5

3

6

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What formula is used to express the sum of integers up to n?

n times n plus two, all over 2

n times n minus one, all over 2

n times n plus one, all over 2

n plus n plus one, all over 2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in a proof by induction?

Prove the formula for k+1

Prove the base case

Prove the induction step

Assume the formula for k

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the base case, what is the sum of integers up to 1?

0

1

3

2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What assumption is made in the induction step?

The formula is true for k

The formula is true for all n

The formula is true for k+2

The formula is true for k-1

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the next step after assuming the formula is true for k?

Prove it for k-1

Prove it for k+2

Prove it for k+1

Prove it for all n

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