perplexus.info :: Sequences : Fibonacci but with Subtraction still stays Positive

Fibonacci but with Subtraction still stays Positive (Posted on 2023-02-15)

Let D[n] be a sequence whose values are recursively related by D[n] = D[n-2] - D[n-1].

D[1] is fixed to be equal to 1. Most choices of D[2] will result in a sequence which eventually has some n such that D[n] is negative.

What is the set of values for D[2] exist such that all terms of D[n] are positive?

See The Solution Submitted by Brian Smith

Rating: 4.0000 (1 votes)

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Solution

| Comment 1 of 3

I believe the only solution is (sqrt(5) - 1)/2 = about 0.6180339887

If x is the second term, the series would be:

x so x>0

1-x so x<1

2x-1 so x>1/2

2-3x

5x-3

5-8x

13x-8

etc

Posted by Larry on 2023-02-15 13:43:48

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