How to demonstrate using the Fibonacci sequence?

Question

The Fibonacci sequence, (fn) n∈N, is defined recursively as follows:
f0 = f1 = 1,
fn = fn-2 + fn-1 (n ≥ 2)

Demonstrate for all n ∈ N:

If n ≥ 1, then fn-1 ⋅fn + 1 = f ^ 2n - (- 1) ^n

 

 

Answer 1

n=1

fib(0)*fib(2) = 1 * 2 = 2

and fib(1)^2 - (-1)^1 = 1 - -1 = 2

n=2

fib(1) * fib(3) = 1 * 3 = 3

and fib(2)^2 - (-1)^2 = 2 - 1 = 1

FALSE

n=3

fib(2) * fib(4) = 2 * 3 = 6

fib(3)^2 - (-1)^3 = 2^2 - (-1)

= 4 + 1 = 5

FALSE

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