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

SL IA Type 1: Infinite Summation Portfolio

Extracts from this document...


Example Math Portfolio SL

Infinite Summation – Type 1:

We being this analysis by investigating series of the type image00.png, where tn represents the nth term in the series, x and a are two parameters that may be varied and n! = n X (n -1) X (n -2) X … X 3 X 2 X 1.

Initially we will consider the summation, Sn where Sn means to sum the first n terms of the series.  We will find the Sn for the

...read more.









To further clarify how these values were obtained a sample calculation is shown below:

image04.png, a screenshot highlighting the formula used in Excel to complete the rest is shown in figure 1 below.


Figure 1: Showing how Excel was used to calculate Sn

If we now take these values and create a graph of n vs. Sn we obtain the result shown in Figure 2

From this graph it is clearly seen that the summation Sn converges on the value 2.  It can be said then that as n approaches infinity the summation converges on the value 2.image06.png

If we complete this same exercise, but this time change the value of parameter a to equal 3 we obtain the following results for Sn shown as a screenshot for Excel.


...read more.


So clearly as the value of a decreases the value of Sn does converge on it, however it does not do so in a smooth systematic way, but rather chaotically.

Now we will try large values of a:

a = 1000


Now it does not converge to the value of a, after 10 steps; however if the value of n is increased the value of Sn does indeed converge on 1000 as shown.  It also appears to do so in a smooth fashion.


We can clearly observe a general trend for Sn in which assuming n is large enough (i.e n approaches infinity) then the value of Sn converges upon the value of a.

...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 Studies I.A

    which about the same as the number of doctors working in the Nigerian public service. Retaining these expensively-trained professionals has been identified as one of the goals of the government. Swaziland Like many subsaharan African countries Swaziland is severely affected by the HIV and AIDS pandemic.

  2. Math IA - Logan's Logo

    From here, it is obvious that a sine function would fit the data. A sine function can be defined as: , Where a represents the amplitude of the sine curve (or vertical dilation); b is the horizontal dilation; c is the horizontal shift; d is the vertical shift; and x and y are the width and length in units respectively.

  1. Math IA type 2. In this task I will be investigating Probabilities and investigating ...

    Adam wins 1.333 of the 2 points and Ben wins 0.667 of the 2 points. This is not practically possible and a limitation to the model. I do not have concerns about its validity other than the fact that the point winning probability will not be constant for all trials.

  2. MATH IA- Filling up the petrol tank ARWA and BAO

    Let's consider the limitations of these 2 equations. First of all the model doesn?t account for time, which is precious, on top of that we have assumed that drivers fuel up at regular intervals of time. But in reality, not all motorist fuel up at regular intervals of time.

  1. Math IA Type 1 Circles. The aim of this task is to investigate ...

    Figure 12. At this point it can be confusing, since the square of OP and two times OP are the same in the case of r = 2. Therefore another value must be tested. In the next case r= 6 and OP = 3.

  2. MATH Lacsap's Fractions IA

    The pattern for the numerator is also only based on a theory that it falls into a quadratic pattern and that it is a perfect math model when plotting the graph.

  1. Infinite Summation- The Aim of this task is to investigate the sum of infinite ...

    S5+t6=9.905847 S7= S6+t7=9.973936 S8= S7+t8=9.993534 S9= S8+t9=9.998548 S10= S9+t10=9.999702 n Sn 0 1 1 3.302585 2 5.953534 3 7.988213 4 9.159468 5 9.698851 6 9.905847 7 9.973936 8 9.993534 9 9.998548 10 9.999702 This diagram shows the relation between Sn and n using the gained results.

  2. SL Math IA: Fishing Rods

    Second, I used the x values of 3 (in the first set) and 6 (in the second set) to once again allow for a broad representation of the data points in the final quadratic equation. Both of these points (3 and 6)

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