ETC…..

From theses first ten terms of the sequence we can derive a formula for in terms of . The formula is:

By plotting the first ten terms of the sequence on a graph, we can study the relation between.

Graph 1

This illustrates the relation between n and L in the case of .

From this graph we can see that the value of L is slowly moving towards the value of aprox. 1,618, but the value of L will never attain this value. If we look at the relation between and we can establish that in the case of .

, when n approaches infinity,

lim() → 0

We can expand this and arrive at another infinite surd with a sequence of:

We can take this sequence and expand it:

ETC…

Graph 2

This graph illustrates G in the case of an.

From this graph we can clearly see that approaches the value of 2, but it never arrives at 2.

Now consider:

As we are dealing with an infinite surd, we can expand this out to get:

This can be expressed as:

From this we can determine:

Comparing this with our graph, we can conclude that our general term is correct!