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Infinite surds

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Introduction

Portfolio assignment:

Infinite Surds

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

The following expresion is an example of an infinite surd:

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

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image25.pngimage26.png

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ETC…..

From theses first ten terms of the sequence

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Middle

.

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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Conclusion

an.

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

Now consider:

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

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This can be expressed as:

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From this we can determine:

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

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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