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Vocabulary
Complete the chart.
Word | Definition |
Mathematical Induction | ________________________________________________________ |
______________ | the total of all of the numbers in a series |
nth term | ________________________________________________________ |
______________ | a number or an expression that is multiplied with other factors to create a product |
______________ | the product of the positive integers from 1 to some value n: n! = 1 × 2 × 3 × 4...× (n-1) × n |
Inequality | ________________________________________________________ |
Postulate | ________________________________________________________ |
Inductive Proofs
Steps of Mathematical Induction:
Step 1) The base case: prove that the statement is true for __________________. Often with induction you may want to expand the first step by showing that the statement is true for several _______________.
Step 2) The inductive hypothesis: assume that the statement is true for ________________.
Step 3) The inductive step: use the inductive hypothesis to show that the statement is true for ______________.
Apply these steps to the integer sum formula:
Step 1) _______________________________________________________________
Step 2) _______________________________________________________________
Step 3) _______________________________________________________________
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Use induction to prove the following:
Induction and Factors
Properties of Integers and their Factors
Complete the properties and prove with induction.
Property 1 : If a is a factor of b , and a is a factor of c , then a is a factor of _____________.
Proof: _________________________________________________________
Property 2 : If a is a factor of b and b is a factor of c , then a is a factor of ____________.
Proof: _________________________________________________________
.
- Without adding, determine if 8 a factor of 56 + 80
- Proove:
- Proove:
- Prove that 3 is a factor of for all positive integers n .
Induction and Inequalities
Describe the following properties of inequalities:
Transitive Property: _________________________________________________
Addition Property: _________________________________________________
Multiplication Property: _________________________________________________
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Prove the following inequalities:
- The side length of a pentagon is less than the sum of all its other side lengths.
- Given: are positive numbers, prove the following:
- for
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