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Maths Infinite Surds

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Introduction

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Previous expression is known as an infinite surd. We can turn the surd in to a following sequence:

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etc.

From the 10 first terms of the sequence we can present the relation of two following terms as:

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Middle

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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

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when n approaches infinity

lim(image04.png) → 0

We

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Conclusion

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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:

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

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

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