Question

Help! I have this question about fibonacci numbers.
The first part of the problem had me figure out how many pairs of rabbits there are after one, two, three months etc... (One pair after one month, one pair after two, two pairs after three, 3 pairs after four, 5 pairs after five ...)

The second part says: (see below)

Answer 1

we could write this sequence as:
\[{1,1....x _{n-2}; x _{n-1};x _{n}....}\]
where n is index of numbers in the sequence. Write an equation to relate \[x _{n},x _{n-1}, x _{n-2}\]

Answer 2

then find the limit where n is a positive integer \[\lim_{n \rightarrow infinity} (x _{n}/x _{n-1})\]
where \[x _{n}\] is the quantity described in the previous part of the problem above. denote quantity by \[\phi \]