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?

When,  D[2] = (-1+sqrt(5))/2 , then all the terms of D(n) are positive.

Edited on February 22, 2023, 2:26 am

Posted by K Sengupta on 2023-02-22 02:25:00