What is the initial step in a proof by induction?

Proof Techniques and Inequalities

Interactive Video
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Mathematics
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9th - 10th Grade
•
Hard

Olivia Brooks
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Assume the statement is false for n equals k
Assume the statement is true for n equals k
Prove the statement for n equals k+1
Start with a known false statement
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of substituting k+1 in the proof?
To verify the base case
To simplify the equation
To establish a new assumption
To extend the assumption to the next case
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to start from a known true statement in a proof?
To make the proof more complex
To ensure the proof is based on a valid foundation
To avoid using assumptions
To introduce new variables
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of multiplying both sides of an inequality by a positive number?
It reverses the inequality
It invalidates the proof
It simplifies the equation
It maintains the direction of the inequality
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can you prove that a number is greater than another in an inequality?
By showing it is greater than a smaller number
By proving it is greater than a larger number
By showing it is equal to a smaller number
By demonstrating it is less than a larger number
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of the extra terms in the inequality proof?
They help show the inequality is valid
They are used to reverse the inequality
They are ignored in the final step
They complicate the proof
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to ensure the extra terms in the proof are positive?
To ensure the terms cancel out
To make the proof more complex
To simplify the proof
To maintain the inequality's direction
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