Concept explainers
Explain how the concept of dominoes can help you understand the power of mathematical induction.
Answer to Problem 39HP
If the first domino falls, then all the dominoes will fall because if any domino falls, it means that the next domino will fall too and so on.
Explanation of Solution
Given:
Explain how the concept of dominoes can help you understand the power of mathematical induction.
Concept Used:
Given a line of closely arranged dominoes, we have: if the first domino falls, then all the dominoes will fall because if any domino falls, it means that the next domino will fall too and so on.
This principle applies to induction: If the statement we have to prove is true for the first element and if the statement being true for one element leads to the statement being true for the next element, then it means the statement is true for all elements.
Thus, if the first domino falls, then all the dominoes will fall because if any domino falls, it means that the next domino will fall too and so on.
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Algebra 2
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