• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Maths Portfolio Infinite Surds

Extracts from this document...

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.

image05.png

The first ten terms of the surd can be expressed in the sequence:

image06.png

From the tem terms of the sequence we can observe that the formula for the sequence is displayed as:


image16.png

The results had to be plotted in a graph as shown below:

image27.png

The graph above shows us the relationship between n andimage10.png. We can observe that as n increases, image10.png 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.

...read more.

Middle

From the tem terms of the sequence we can observe that the formula for the sequence is displayed as:


image08.pngimage09.png

The results had to be plotted in a graph as shown below:

The graph above also shows us the relationship between n andimage10.png. We can observe that as n increases, image10.png 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

image00.pngimage11.png

image03.pngimage04.png

image12.png

image13.png

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

image14.png

...read more.

Conclusion

image30.pngimage29.png

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 equationimage31.png. By rearranging the formula to make k the subject I came to the conclusion that image32.png, the general statement.

...read more.

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

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Math Portfolio type 1 infinite surd

    Thus: Consider another infinite surd: The first term is Calculate the decimal values of the first ten terms of this sequence: Using MS Excel 2008 Terms Values 1 1.847759065 2 1.961570561 3 1.990369453 4 1.997590912 5 1.999397637 6 1.999849404 7 1.999962351 8 1.999990588 9 1.999997647 10 1.999999412 11 1.999999853 12

  2. Solution for finding the sum of an infinite sequence

    And is defined as the sum of the first term. In this case, , meaning the value will keep increasing, but the will increase up to 4 unit, and then it will remain constant. It won't go further than 4.

  1. Infinite Summation - In this portfolio, I will determine the general sequence tn with ...

    When x = 3 and a = 5: Sn = e3ln5 = 125 = 53 When x = 4 and a = 5: Sn = e4ln5 = 625 = 54 ==> That is so interesting, that I noticed : - Tn (a,x)

  2. Infinite Surds Investigation. This graph illustrates the same relationship as was demonstrated in the ...

    These values are shown in bold in the table above. Using those values, I can check to see if they will, in fact, make the expression , an integer: This table of values shows the some of the other of the values of the expression, that I calculated by making

  1. Mathematics (EE): Alhazen's Problem

    Extending the line OA and OB, we obtain the chords OA' and OB'. Consider the angles that these legs form with the radius OC, angles ? and � - if ball A is to rebound and strike ball B then ?

  2. Math Portfolio: trigonometry investigation (circle trig)

    340 -0.3420201 0.939693 -0.3639702 -0.36397023 360 -2.45E-16 1 -2.45E-16 -2.4503E-16 As can be clearly seen in the table above, the values for tan? and are identical. Further to prove this, I used TI 83 calculator for better explanation such as random numbers.

  1. Infinite Surds

    infinite surd where the first term is , find an expression for the exact value of this general infinite surd in terms of k. ANSWER: The formula in terms of k � = The value of an infinite surd is not always an integer.

  2. Infinite Surds

    an+1 = <-- Get rid of the subscripts. (a = 2<-- Square it to get rid of the radical sign. a2 = k + a<-- Get all numbers on one side. Then set them equal to 0. a2 - a - k = 0<-- One now uses the quadratic formula because this is unable to be factored.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work