Question

Asked Dec 19, 2019

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The Fibonacci sequence has many unusual properties. Experiment to decide which of the following properties are valid. *Note*: *F*_{n} represents the *n*th Fibonacci number.

5F_{n} − 2F_{n − 2} = F_{n + 3} for n ≥ 3

valid

not valid

Step 1

Consider the given series known as Fibonacci sequence. Series starts with 0, 1 and then each next term is written as the summation of previous two terms.

Hence, the most common sequence becomes 0, 1, 1, 2, 3, 5, 8, 13, 21…...so on

Step 2

We will check it in two ways, first let’s do it in short way using a small value of ‘n’.

Le...

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