Mathematics Quiz on Principle of Mathematical Induction
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Preview questions
1. What is the first step in proving a statement using mathematical induction?
Assume the statement is true for n=k · Verify the base case · Prove the statement for n=k+1 · Identify the statement to prove
2. If P(n) is a statement that is true for n=1, what is the next step in induction?
Show P(k) is true for k > 1 · Show P(k) is true for k = 1 · Show P(k+1) is true assuming P(k) is true · Show P(k) is false
3. In mathematical induction, what does the base case establish?
The validity for all integers · The validity for the first integer · The validity for the last integer · The validity for all even integers
4. Which of the following statements is true regarding the principle of mathematical induction?
It can only be used for even numbers · It requires proving an infinite number of cases · It only applies to natural numbers · It can be used for any type of number
5. If P(n) is true for n=k, what must be shown for induction to be complete?
P(k) is false · P(k+1) is true · P(k) is true · P(k-1) is true
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