Maths Infinite Surds

As we can see from the graph the value of L slowly moves toward value of approximately 1,618 or so, but will never actually reach it. If we furthermore consider what this shows about the relation between  and , we can determine that in the case of

when n approaches infinity

lim() → 0

We can expand our point by taking another sequence build from infinite surd as an example. Let our

sequence be following.

etc.

Graph 2 illustrates G in the case that

From here we can easily see that  approaches value of 2 but never quite reaches it. Let us now consider a general example:

Because of the fact that we are working with an infinite surd:

And from here we can deduce by using the null factor law the expression for any value of k which expression forms an integer. Examples:

Because we know that the expression is positive we can determine that

When we compare this result to our results present in the graph to we can determine that our general term works.