Prove the given property of numbers directly from the definition (hint: do a direct proof): (1 point) F(n + 3) = 2F(n + 1) + F(n) for n >=0 Solution You haven\'t specified what [F(n)] is, but I\'m assuming it\'s the nth Fibonacci number. The direct proof is as follows. [F(n+3)=F(n+2)+F(n+1)=F(n+1)+F(n)+F(n+1)] [=2F(n+1)+F(n)] where [F(n+3)=F(n+2)+F(n+1)] and [F(n+2)=F(n+1)+F(n)] are true by the definition of the Fibonacci sequence..

1. Prove the given property of numbers directly from the definition (hint: do a direct proof): (1
point)
F(n + 3) = 2F(n + 1) + F(n) for n >=0
Solution
You haven't specified what [F(n)] is, but I'm assuming it's the nth Fibonacci number. The
direct proof is as follows.
[F(n+3)=F(n+2)+F(n+1)=F(n+1)+F(n)+F(n+1)]
[=2F(n+1)+F(n)]
where [F(n+3)=F(n+2)+F(n+1)] and [F(n+2)=F(n+1)+F(n)] are true by the definition of the
Fibonacci sequence.