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We have seen that the minimum number H, to move a Tower of Hanoi with n disks from the left-most peg to the right-most peg is H, = 2" – 1, where we argued via induction. We have also seen that H, satisfies Hn+1 = 2H,n + 1. Use the method of linear nonhomogeneous recurrence relation to obtain the same formula. (Hint: The recurrence relation is of degree 1, so its homogeneous part has a characteristic equation that is linear. For the particular solution ph, use the guess-form A+ Bn. Also recall that H1 = 1.)

We have seen that the minimum number H, to move a Tower of Hanoi with n disks from the left-most peg to the right-most peg is H, = 2" – 1, where we argued via induction. We have also seen that H, satisfies Hn+1 = 2H,n + 1. Use the method of linear nonhomogeneous recurrence relation to obtain the same formula. (Hint: The recurrence relation is of degree 1, so its homogeneous part has a characteristic equation that is linear. For the particular solution ph, use the guess-form A+ Bn. Also recall that H1 = 1.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 57EQ
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7. We have seen that the minimum number H„ to move a Tower of Hanoi with n disks from the left-most peg to the right-most peg is H, = 2" – 1, where we argued via induction. We have also seen that H, satisfies Hn+1 = 2H,, +1. Use the method of linear nonhomogeneous recurrence relation to obtain the same formula. (Hint: The recurrence relation is of degree 1, so its homogeneous part has a characteristic equation that is linear. For the particular solution ph, use the guess-form A + Bn. Also recall that H1 = 1.)
Transcribed Image Text:7. We have seen that the minimum number H„ to move a Tower of Hanoi with n disks from the left-most peg to the right-most peg is H, = 2" – 1, where we argued via induction. We have also seen that H, satisfies Hn+1 = 2H,, +1. Use the method of linear nonhomogeneous recurrence relation to obtain the same formula. (Hint: The recurrence relation is of degree 1, so its homogeneous part has a characteristic equation that is linear. For the particular solution ph, use the guess-form A + Bn. Also recall that H1 = 1.)
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