Answer to Question #241957 in Math for Lia

Question

Binets formula is being use in determining unknown Fibonacci numbers because they are difficult to determine using the manual method

Answer 1

The explicit formula for the terms of the Fibonacci sequence,  $Fn=\frac{(\frac{1+√5}{2})^n−(\frac{1−√5}{2})^n}{√5}$ has been named in honor of the eighteenth century French mathematician Jacques Binet, although he was not the first to use it. Typically, the formula is proven as a special case of a more general study of sequences in number theory. However, we shall relate the formula to a geometric series.