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December 1st, 2018, 12:29 PM  #1 
Newbie Joined: Nov 2018 From: France Posts: 8 Thanks: 0  Recursive definition and induction
Hey. The series $a_n$ is defined by a recursive formula $a_n = a_{n1} + a_{n3}$ and its base case is $a_1 = 1 \ a_2 = 2 \ a_3 = 3$. Prove that every natural number can be written as a sum (of one or more) of different elements of the series $a_n$. Now, I know that is correct intuitively but I don't know how to prove that. Generally, I have some problem of understanding the concept of recursion. Thanks. 
December 1st, 2018, 01:01 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,821 Thanks: 723 
Statement is not clear. Every number is $a_1+a_1+a_1+.....$

December 1st, 2018, 01:09 PM  #3 
Newbie Joined: Nov 2018 From: France Posts: 8 Thanks: 0  
December 2nd, 2018, 07:25 PM  #4  
Senior Member Joined: Sep 2016 From: USA Posts: 642 Thanks: 406 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
Write out more terms from this sequence and its obvious.  

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definition, induction, recursive 
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