Using mathematical induction to prove a formula

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Mathematics
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11th Grade - University
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Hard
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7 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in proving a statement using mathematical induction?
Prove the statement for n = k + 1
Assume the statement is true for n = k
Prove the statement for n = 1
Prove the statement for n = 0
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the induction hypothesis, what do we assume?
The statement is true for n = k + 1
The statement is false for n = k + 1
The statement is false for n = k
The statement is true for n = k
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the goal of the induction step in mathematical induction?
To prove the base case
To prove the statement for n = k + 1
To find a counterexample
To disprove the statement for n = k
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do we transition from S(k) to S(k+1) in the induction step?
By multiplying S(k) by 2
By dividing S(k) by 2
By subtracting the previous term from S(k)
By adding the next term to S(k)
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the variable 'n' represent in the general formula?
The product of terms
The number of terms
The sum of terms
The difference of terms
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to distinguish between 'n' and 'k' in mathematical induction?
To ensure the formula is correct
To simplify the calculations
To avoid confusion between the base case and the induction step
To make the proof more complex
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of using 'k' in the induction hypothesis?
To represent the initial term
To represent an arbitrary term
To represent a specific term
To represent the final term
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