Recitation Mathematical Induction

What does the principle of mathematical induciton state

• if the base case (for n = 1) is true and inductive step is true, then the theorem holds for all positive integers

• if the base case (for n = 1) is true and inductive step is false, then the theorem holds for all positive integers

• if the base case (for n = 1) is false and inductive step is true, then the theorem holds for all positive integers

• if the base case (for n = 1) is false and inductive step is false, then the theorem holds for all positive integers

What is the answer when n = 5

• 45

• 50

• 54

• 55

• 3

• 2

What value of n will satisfy the base case?

• 0

• 1

• 2

• 3

What is the inductive hypothesis in the inductive step

• The process of proving that P(k+1) is true

• The assumption that if P(k+1) is true, then the statement is true

• The assumption that k is an integer

• The assumption that the original statement is True

What is the base case to prove that for any non-negative integer n ≥ 96, (1.1)n ≥ n2

• 0

• 1

• 96

• 97

What is the value of the base case of this equation

• 0

• 1

• 3

What must be proven in the inductive step?

• Prove that the base case is true

• Prove that k is in the same domain as n

• Prove that, assuming k is true, k+1 is true

• Prove that the process of induction is beyond our understanding and that only the math gods can help us now

What is the value of the base case when trying to prove that for any positive integer n, 7 evenly divides 9n - 2n.

• 7

• 14

• 1

• 0

What are Triominoes

• Three dominoes

• Dominoes with three blocks instead of two

• vegan Domino's pizza

• Triangular dominoes

• A fancy cheese