• 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...

Introduction

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.

√1+√1+√1+√1+…

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.

Middle

image00.png

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.

Conclusion

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. Math Portfolio type 1 infinite surd

    From [1] and [2] we have: Hence the general statement for k is a product of two consecutive integers. Checking the general statement that represents all the values of k for which the expression is an integer using the 1st method.

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

    = t0 + t1 + t2 = = 13.274749 T4 (1.5, 10) = t0 + t1 + t2 + t3 = = 24.384625 T10 (1.5, 10) = t0 + t1 + t2 + t3 + t4 + t5 +

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

    The amount of drug in the bloodstream increases and decreases repeatedly. Method I started by entering the data given up to the sixth hour. At the sixth hour, I added 10 to the left over amount of drug in bloodstream.

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

    x = Only the positive value is accepted. As shown in Discovery 2b page 9, an infinite surd can be an integer. Since represents the general exact form for all infinite surds, we can throw in values for k to find values that make the expression an integer.

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

    This is similar to what has happened with the previous example. The chart below describes the difference between an and an+1 as the value of n increases. Difference of an and an+1 an - an+1 Decimal value rounded to the exact billionth a1-a2 -0.1138114958 a2-a3 -0.028798892 a3-a4 -0.007221459 a4-a5 -0.001806725

  1. Investigating Slopes Assessment

    However, before, arriving to this conclusion, I had to analyse my results of the 3rd case. In fact, I can state that when, in this case, f(x)= X5 it means that f1(x)= 5X4 So, as my final conclusion for the first part of investigation number two, I can clearly compare

  2. Infinite Surds investigation with teacher's comments.

    The graph will then follow a straight horizontal line. In other words, as n approaches infinity, the value of an- an+1 approaches 0. To express in numerical notations, as n??, an=an+1. Use your results to find the exact value for this infinite surd.

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