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

Infinite Surds portfolio

Extracts from this document...


Internal Assessment number 1

Nazha AlFaraj

Ms. Leana Ackerman

IB Mathematics SL (year 2)

Sunday, February 19, 2012

Infinite Surds

This following expression is known as an infinite surd.


The previous infinite surd can be changed into the following sequence:

a1= √1+√1= 1,414213

a2= √1+√1+√1= 1,553773

a3= √1+√1+√1+√1= 1,598053

a4= √1+√1+√1+√1+√1= 1,611847

a5= √1+√1+√1+√1+√1+√1= 1,616121

a6= √1+√1+√1+√1+√1+√1+√1= 1,617442

a7= √1+√1+√1+√1+√1+√1+√1+√1= 1,617851

a8= √1+√1+√1+√1+√1+√1+√1+√1+√1= 1,617977

a9=√1+√1+√1+√1+√1+√1+√1+√1+√1+√1= 1,618016

a10= √1+√1+√1+√1+√1+√1+√1+√1+√1+√1= 1,618028

The first 10 terms can be represented by:

an+1= √1 + an

If we

...read more.



The data begins to increase by a smaller amount about each consecutive n, suggesting
that the data may be approaching as asymptote. As these values get very large, they willprobably not get much higher than the value of a10, because there already appears to bealmost horizontal trend. The data also suggests that the asymptote is between the value of 6 and seven, although to find the exact value requires a different approach

...read more.


x²= √k+√k+√k…²

x²= k+ √k+√k+√k…

Because we are working with an infinite surd we can deduce that:

x² = k + x

0= k + x – x²

0 = (x+k)(x-k)

The null factor law can be used to portray that any value of k represents an integer.

(x + 4) (x – 4) = 0

→ x² - 4x + 4x – 16 = 0

→ x² - 16 = 0

→ x² = 16

→ x = 4

 As we compare this result to the general statement we provided we can easily establish that our general statement is valid.

...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. IB Mathematics Portfolio - Modeling the amount of a drug in the bloodstream

    With no buildups from previous doses, the amount at the end of the first dose would be the lowest. 4. What would happen to the values during these periods? (a) No further doses are taken If no further doses are taken, then according to the model chart, the amount of

  2. Math IA, Infinity surd

    a = 1 � 1+4k 2 The pattern dictates that the answer must be positive, unless the value of "k" is less then zero. But it's impossible in this case because negative number in a square root is not a real number.

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

    those what numbers, when divided by two, would make the expression an integer. So, to find values that would make k a perfect square, I would set: , , , and so on... Example Solution for k: This table of values shows several the solutions for k using perfect square:

  2. 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

  1. Infinite surds portfolio - As you can see in the first 10 terms of ...

    The value of the infinite surd which is about 1.61803 can be considered as x. So, let x be: x = (x)2 = 2 Square both sides to create an equation to work with. x2 = The infinite surd continues.

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

    So it suggests that Sn will be in domain 1 Sn 3 as n approaches . Above, I have been supposing that the greatest value for the sum of infinite sequence Sn is a. And I want to check if it's correct with some different values of a.

  1. Infinite Surds investigation with teacher's comments.

    are plotted in the graph below showing the relationship between n and an. * Specify technology? (Graph) By plotting the relation between n and an, we can observe that there is a positive relationship between n and an. That is, as n increases, an also increases.

  2. Investigating Slopes Assessment

    -32 X= -1 Y= -4x+(-3) -4 X= 0 Y= 0 0 X= 1 Y= 4x+(-3) 4 X= 2 Y= 32x+(-48) 32 Again, with these point, I can say by looking at the gradient, that f1(x)= 4X3. Now, I?m starting to have a brief supposition of what my general discussion and results for investigation number 2 will be.

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