Let F, F₁, F2, ... denote the Fibonacci sequence. Find an expression for (Fk+ 1)² – (FK)² a sequence. For every integer k ≥ 1, (Fk+ 1)²-(F) ² (Fk+1 = 1-FH([ (Fk+1) -FR)([ Thus, Fk+1-Fk= Applying the definition of the Fibonacci sequence a second time gives that Fk + 1 = F₁ + Fk (**) by the formula for a difference of two squares as a product of two values of the (*) by definition of the Fibonacci sequence. Substituting (**) into (*) gives that (Fk+ 1)² - (FK)² = Fk-1) ( [

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