Describe the Fibonacci sequence recursively: Include Initial conditions; (2 marks)
Write a recursive algorithm for computing Fibonacci numbers: (3 marks)
The 'golden ratio' is 1+√5, one of its properties is that √5 = (1+√5)/2, and hence (√5 - 0) = (1 - 0)√5.
Show by mathematical algebra that pk+0k-1 = (1 - 0)k-1 * (1 - √5)k = 0k+1 * (1 - 0)k+1 for any positive integer k. (1 mark)
Use induction to prove that the Fibonacci numbers can be computed by using the Strong golden ratio using the following formula: Fₙ = (1-√5)⿠/ √5