Proof by Induction
Quiz
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Medium
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6 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove. What is the first?
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
According to the principle of mathematical induction, to prove a statement that is asserted about every natural number n, there are two things to prove. What is the second?
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The second part (If the statement is true for n = k, then it will be true for its successor, k + 1) contains the induction assumption. What is it?
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The sum of the first n odd numbers is equal to the nth square.
1 + 3 + 5 + 7 + . . . + (2n − 1) = n2
To prove this by mathematical induction, what will be the induction assumption?
1 + 3 + 5 + 7 + . . . + (2k − 1) = k2
2x1 − 1 = 12
1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
1 + 3 + 5 + 7 + . . . + (2n − 1) = n2
On the basis of this assumption,
[The statement is true for n = k:
1 + 3 + 5 + 7 + . . . + (2k − 1) = k2]
What must we show?
2x1 − 1 = 12
1 + 3 + 5 + 7 + . . . + (2k − 1) = k2
1 + 3 + 5 + 7 + . . . + (2k − 1) + (2k + 1) = (k + 1)2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let S(n) = 2n − 1. Evaluate:
a) S(k)
b) S(k + 1)
b) S(k + 1) = 2n + 1
b) S(k + 1) = 2k + 1
b) S(k + 1) = 2k + 1
Tags
CCSS.HSF.IF.A.2
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