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Maths Infinite Surds

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












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


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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


when n approaches infinity

lim(image04.png) → 0


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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:


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.

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