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

    + = 6.998638 S9 = S8 + t9 = 6.998638 + = 6.999740 S10 = S9 + t10 = 6.999740 + = 6.999956 Using Microsoft Excel, I plot the relation between Sn and n: n Sn 0 1 1 2.945910 2 4.839193 3 6.067246 4 6.664666 5 6.897171 6 6.972577

  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

    Evaluation: As the graph shown, as the n gets very large, the values of an still be the same. Hence the value of is equal to 0. According to the data table, after the 4th term, all the data have the same until 1.61 which is 2 decimal place.

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

    So as n gets larger, an- an+1 gets closer to 0. Since the sequence goes on forever, it cannot be determined if an- an+1 ever equals 0. From previous results, you know that as n, an gets flatter and levels out right under about 1.61803.

  2. This portfolio will investigate the patterns and aspects of infinite surds. Technologies, graphs, and ...

    Base on this, we can predict that as the value of n becomes vey large, , and we can come up with an expression that represents as n approaches infinity. 4 Equation for When 5 Solving the Sequence 6 To prove that the previous methods used are true for all infinite surds, we can apply them in a different situation.

  1. Investigating Slopes Assessment

    I decided to use them again because I know they are correct, since they worked out for two investigations. My function I will now analyse, this time, will now be f(x)=X2×X3. From the previous cases I can now exactly say that the conjecture about f1(x)

  2. Infinite Surds investigation with teacher's comments.

    That is, as n increases, an also increases. However, the increase of an is not proportional to the increase of n. an increases at a decreasing extent. That is, each time it increases less than before. The scatter plot seems to have a horizontal asymptote at y=2. The value of an approaches approximately 2 (i.e.

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