Concept explainers
Describe how you would use mathematical induction to prove
What happens when n - 1? Write the statement that we assume to be true. Write the statement that we must prove. What must be done to the left side of the assumed statement to make it look like the left side of the statement that must be proved? (More detail on the actual proof is found In Exercise 85.)
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COLLEGE ALGEBRA-MYMATHLAB 18 WEEK >I<
- Tower of Hanoi The result in Exercise 39 suggest that the minimum number of moves required to transfer n disks from one peg to another is given by the formula 2n1. Use the following outline to prove that this result is correct using mathematical induction. a Verify the formula for n=1. b Write the induction hypothesis. c How many moves are needed to transfer all but the largest of k+1 disks to another peg? d How many moves are needed to transfer the largest disk to an empty peg? e How many moves are needed to transfer the first k disks back onto the largest one? f How many moves are needed to accomplish steps c, d, and e? g Show that part f can be written in the form 2(k+1)1. h Write the conclusion of the proof.arrow_forwardProve by induction that 1+2n3n for n1.arrow_forwardMathematical induction is a method of proving that a statement P(n) is true for all ________ numbers n. In Step 1 we prove that _________ is true.arrow_forward
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