Question

A sequence is defined as an=F n+1/Fn, n>1, where Fn is a member of the Fibonacci sequence.

a) Write down the first 10 terms of an

b) Show that an=1+1/a n-1

Answer 1

do you know the property of Fibonacci numberline ?

Answer 2

The Fibonacci sequence is defined as

\[F _{n} = F _{n-1}+ F _{n-2}\]

with

\[F _{1}= 1\] and

\[F _{2}=1\]

As \[n > 1\]

The series
\[a _{n}\]
will start with\[n=2\]

To prove part (b), use the proof by induction.