Let F(n) denote the Fibonacci numbers. Prove the following property for n ≥ 3 directly from the definition for F(n). F(n+1) + F(n-2) = 2F(n)

Define the Fibonacci numbers as Fo= 0, F₁ = 1 and for n ≥ 2, set Fn = Fn-1+Fn-2. Show that Fn+1Fn-1 − F2 = (-1)" for n ≥ 1 and use this to deduce that gcd(Fn, Fn-1) = 1 for all n ≥ 1.

From course, Number Theory

For the recursively defined function T(n)= ST(1/2) + 3 Which of the following best reflects the two statements: A) T (n) =_-_ (nlgn) B) T(n) = O(2.25) A. Only A is TRUE B. Only B is TRUE C. Both A and B are TRUE D. Both A and B are FALSE