Fibonacci Identities

Math 242 Modern Computational Mathematics

Preliminary Code

Here is one of our fibonacciList modules from last class:

fibonacciList[n_]:=Module[{fibList=Table[0,n+1]},
(* set the initial values (Subscript[F, 0]) and (Subscript[F, 1]) *)
fibList[[2]]=1;

(* compute (Subscript[F, 2]) through (Subscript[F, n]) and store them in the list *)
Do[
fibList[[i]]=fibList[[i-1]]+fibList[[i-2]]
,{i,3,n+1}];

(* return the list *)
fibList
]

Last time, we computed (Subscript[F, n+1])(Subscript[F, n-1]) and ((Subscript[F, n])^2) for various n. What did we observe?