Formula Using Fibonacci Numbers Let be the nth term of the sequence defined recursively by
and let . Find a formula for in the terms of the Fibonacci numbers . Prove that the formula you found is valid for all natural numbers .
A formula for in the terms of the Fibonacci numbers , is valid for all natural numbers .
be the nth term of the sequence. It is defined recursively as
The Fibonacci numbers , , , are defined as follows,
Here, denotes natural numbers.
The Fibonacci sequence is given by,
The nth term of a sequence is defined as follows,
So, the terms of this sequence are as follows,
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started