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# Maths Portfolio Infinite Surds

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Introduction

Maths Portfolio

SL Type 1

Infinite Surds

In this mathematics portfolio we are instructed to investigate different expression of infinite surds in square root form and then find the exact value and statement for these surds.

INFINITE SURDS

The following expression is an example of an infinite surd. The first ten terms of the surd can be expressed in the sequence: From the tem terms of the sequence we can observe that the formula for the sequence is displayed as: The results had to be plotted in a graph as shown below: The graph above shows us the relationship between n and . We can observe that as n increases, also increases but each time less than before, suggesting that at a large certain point of n it stops increasing and just follows in a straight line.

Middle

From the tem terms of the sequence we can observe that the formula for the sequence is displayed as:  The results had to be plotted in a graph as shown below:

The graph above also shows us the relationship between n and . We can observe that as n increases, also increases but each time less than before, suggesting that at a large certain point of n it stops increasing and just follows in a straight line.

To find the exact infinite value for this sequence we would use the equation and rearrange in the correct way to find the value.

Finding the exact value for the surd      The exact value for the surd is 2 as the second answer does not fit in the problem

The general infinite surd in terms of k Conclusion  The results show us that the limitations found in the general statement are those that didn’t give an integer as a final answer. Therefore k has to be an integer, however not a decimal or a fraction as results wouldn’t be a whole number. It also isn’t possible to obtain an integer if k is a negative number because there is no square root for a negative number. For a pleasing result, 1+4k , needs to give a number that possesses a perfect square root, an integer.

I arrived at this general statement by subtracting the n term from the k, and like that finding out that the product of this subtraction is the n term to the power of 2. Like that I found the equation . By rearranging the formula to make k the subject I came to the conclusion that , the general statement.

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

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