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Infinite surds

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Portfolio assignment:

Infinite Surds

First of all, roots that are irrational are called surds.

The following expresion is an example of an infinite surd:


From the previous expresion, generraly know as an infinite surd, we can create the following sequence:










From theses first ten terms of the sequence

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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

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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!

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