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February 14th, 2012, 06:08 AM  #1 
Newbie Joined: Oct 2009 Posts: 14 Thanks: 0  Induction  prove that an explicit function is correct
The task: Write down an explicit definition of the function h, where h(0) = 0 and h(n + 1) = 3 * h(n) + 1. (Hint: compare to the sequence 1, 3, 9, 27, 81, ....) Use induction to prove that your formula is correct. So, I found out that a function f(n) = (3^n  1) / 2 is the explicit function describing the function h (please correct me if I am wrong). The problem now is to prove that the function I found is correct. I have figured out the base step, I think, which was to show that h(1) = f(1). But about the induction step, am I suppose to show that h(n+1) = f(n+1) ? 
February 14th, 2012, 11:31 AM  #2  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 928 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Induction  prove that an explicit function is correct Quote:
 

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