Hi
Hey, I would like some help with this question:
A recursive sequence is a sequence where the th term, , is defined in terms of preceding terms, , etc
one of the most famous recursive sequences is the Fibonacci sequence, created by Leonardo Pisano (1170-1250). The terms of this sequence are define as follows where
It asks me to graph some things, did those, but then it asks me to write an expression, using a limit, to represent the value of the ratios of consecutive terms of the Fibonacci sequence. How would I go about doing this?
Thanks in advance.
Setting the sequence of the is generated recursively by the relation...
(1)
... that is equivalent to the difference equation...
(2)
The (2) indicates that the limit when n tends to infinity of the is given by the positive solution of the equation...
(3)
... so that is...
(4)
The constant is known as 'golden ratio'...
Kind regards