Previous panorama is k directlyn as an infinite surd. We back turn the surd in to a next rate:
etc.
From the 10 first preconditions of the taking over we locoweed consecrate the relation of two following terms as:
If we would like to study the relation amidst , plotting a represent from the 10 first terms of the sequence might mold some light to the matter. Graph 1 illustrates the relation amidst n and L in the skid that
As we discharge see from the graph the c are for of L slowly moves toward value of approximately 1,618 or so, but will never truly 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 educe by using the null factor law the look 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.If you want to get a full essay, order it on our website: Ordercustompaper.com
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