Fibonacci numbers

Definition: A series of numbers in which each number ( Fibonacci number ) is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc.

Illustration 1:-                                                           

Solution 

Adding these we get,

2)Prove that if d | n, then Fd | Fn.

Where F denotes Fibonacci numbers 

Questions:-

1)The Fibonacci sequence is the list of numbers that begins 1, 2, 3, 5, 8, 13 and continues with each subsequent

number being the sum of the previous two.

Prove that when the first n elements of the Fibonacci sequence are alternately added and subtracted, the result is

an element of the sequence or the negative of an element of the sequence. For example,

1−2+3−5 = −3,

and 3 is an element of the Fibonacci sequence.