• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8

# Mathematics portfolio on Infinite Surd

Extracts from this document...

Introduction

Mathematics Portfolio

Standard Level Type I

Infinite Surds

Germaine An

A surd is a sum with one or more irrational number expressed with a radical sign as addends. Examples are 1+√3, √2+√3, and √(1+√(1+√1)). Therefore, an infinite surd has an infinite number of such addends. An example is in the diagram.

The following expression is an example of an infinite surd.

Consider this surd as a sequence of terms an where:

==1.414213562

==1.553773974

==1.598053182

==1.611847754

==1.616121207

==1.617442799

==1.617851291

==1.617977531

==1.618016542

==1.618028597

According to the result, you can aware that a2 =

Then analyzing the formula, an+1 =

On the graph, it represents that at the point of the beginning it raises rapidly as acceleration. However, after that, an-an+1

Middle

So,

1.618033989

Consider another infinite surd

where the first term is

Repeat the entire process above to find the exact value for this surd.

==1.847759065

==1.961570561

==1.990369453

==1.997590912

==.1999397637

==1.999849404

==1.999962351

==1.999990588

==1.999997647

==1.999999412

According to the result, you can aware that  =

Then analyzing the formula, =

This graph shows us that there is a huge change between 1 and 2. And it is constant from 4.  . bn and -

Conclusion

The value of an infinite surd is not always an integer

2=1x2

6=2x3

12=3x4

20=4x5

30=5x6

These are proved, using this formula k= n (n+1)

5(5+1) = 30

5th term which is also described as 5x6=30

Test the validity of your general statement using other values of k.

First off, the formula is k= n (n+1)

Apply

8x9=72----y =

=46

88x89=7832------

=89

222x223=49506---------

=223

And so on..

It is able to notice that

When k is 72, y =  =46

Discuss the scope and/or limitations of your general statement.

According to this, we’ve found that value of K and n always are

n

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

# Related International Baccalaureate Maths essays

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

It should have a small decrease. The suitability of this graph is good. The r2 is .9942. The r2 being .9942 allows me assume that the trend line fits very well near actual data points. From just looking at the graph it self, it looks like most of the data points are on the line.

2. ## Math Portfolio: trigonometry investigation (circle trig)

The value of y equals a positive number on the positive y axis and the value of r equals a positive number as mentioned beforehand. Therefore, when the value of y is divided by the value of r, a positive number is divided by a positive number resulting to a positive number.

1. ## Math Portfolio Type II

(un, rn) = (60000, 1) according to the description. We can get the equation of the linear growth factor by entering these sets of ordered pairs in the STAT mode of the GDC Casio CFX-9850GC PLUS. The STAT mode looks as follows: - Thus, we obtain a linear graph which can be modeled by the following function: - y

2. ## Infinite Summation Portfolio. I will consider the general sequence with constant values

The graph should look like this: 0 1 1 1,69314718 2 1,93337369 3 1,9888778 4 1,99849593 5 1,99982928 6 1,99998332 7 1,99999857 8 1,99999989 9 1,99999999 10 2 Table 2: Shows the values of the graph of against of After using the computer programme Graphmatica, the result of the graph

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

again plot the relation between Sn and n: n Sn 0 1 1 2.098612 2 2.702087 3 2.923080 4 2.983777 5 2.997113 6 2.999555 7 2.999938 8 2.999991 9 2.999997 10 2.999998 Again, I noticed that when and , the values of Sn increase as values of n increase, but don't exceed 3.

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

k=2: This also checks out, since in Part 2 I got the same expression for an In order to find some values of k that would make the expression an integer, I would have to consider what numbers would make the part of the equation a perfect square, and from

1. ## SL Type I Mathematics Portfolio

The ratio test is the most comprehensive, and useful test. If a) Is less than 1, the sequence converges. b) Is greater than 1, the sequence diverges c) Is equal to 1, the test fails to give conclusive information We can use the ratio test to determine whether or not our sequence is converging.

2. ## Infinite Surds investigation with teacher's comments.

* Need elaboration an+1=k+an … x=k+x. So, x2=k+x x2-x-k=0 Using the quadratic formula, x =-b±b2-4ac2a=-(-1)±(-1)2-41(-k)2(1)=1±1+4k2 1+1+4k2 for every value of k ∈ Q+ ________________ An integer is an entire number, and can be written without a fractional or decimal component.

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