Define a sequence, for n ∈ N, as follows: x_1 = m x_(n+1) = (x_n)/2 if x_n is even              = (x_n) + 1 if x_n is odd   Use (strong) induction to prove that, no matter what natural number m you start with, the sequence eventually becomes 1, 2, 1, 2, 1, 2, . . ..

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.5: Mathematical Induction
Problem 29E
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Define a sequence, for n ∈ N, as follows:

x_1 = m

x_(n+1) = (x_n)/2 if x_n is even

             = (x_n) + 1 if x_n is odd

 

Use (strong) induction to prove that, no matter what natural number m you start with, the sequence eventually becomes 1, 2, 1, 2, 1, 2, . . ..

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