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

Infinite summation

Extracts from this document...


Portfolio Task        Infinite Summation ( Type 1 ) Gizem Özgören



1) Consider the following sequence of terms un , where


U1 =

U2 =

U3 =


This question is about infinite summation, which is a way of expressing an infinite sum. The series consist of (n) terms where (n) effects the sum. The question challenges us to learn about series on ourselves and help us academically in further tasks / exams.

(i) Find an expression for un, in terms of n.

        In this question, we are asked to find an expression for un  , so what we have to do is to find a formula which may be applied to all the terms of the sequence and that will help us understand how (n) effect the terms.

First of all, we should start by giving the name un to the formula.

        Un =

...read more.


image00.png .

Now, we are asked to put in the n values according to the given domain (image01.pngimage01.png and calculate the summation.

We should start with writing down all the terms that are suitable with the domain, calculate their value (using TI) and then calculate the summation. In addition, we should note that the answer should be in 6 decimal places, so the values of the terms should also be in 6 decimal places.

U0 =

U1 =

U2 =

U3 =

U4 =

U5 =

U6 =

U7 =

U8 =

U9 =

U10 =

Now, it is time to add all the terms up and in order to calculate accurately, I will use a TI.

Sn = u0 + u1 + u2 + u3 + u4 + u5+ u6 + u7 + u8 + u9 + u10

S10 =

(iii) Using technology, plot the relation between Sn and n.

...read more.


 according to that in n.


Summation (Sn )























After  calculating the summation and graphing it, I saw that the bigger n gets, so does Sn. The reason why is that the function grows exponentially and everytime you add up a new value, the summation increases. n and Sn  directly proportional terms.

In conclusion, throughout the first question, I defined what an infinite summation is, found ways to express a series as a function, what permutation is and why we use it in order to create a function for the sequence, what the summation of the given sequence is and finally, how the factor n ( number of terms in the sequence ) effects the summation. I came to the answer that as n gets larger,  by several interrogations such as calculating the values of each term, adding them up, graphing the data which lead met o the answer that in an infinite summation,

...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. SL Type 1 PF - Infinite Summation - A general statement has been reached, ...

    This leads to a general statement about the tendency of each equation. This leads to a general statement: In final statement of the general traits discovered in this assignment, the values of in the sums of the infinite sequences are accountable for the precision of the sums to the value of .

  2. Infinite Summation

    Profilex..."MHa�����-��$T& R�+S�e�L b�}w�g�(tm)�-E""�u�.VD��N�C�:D(tm)u� �E^"��;""cT3/403�y���|1/2�U�R�cE4`��"�ÞvztL�U�F\)�s:��(c)��k�-iYj"��6|"v(tm)P4*wd>,y<��'/�<5g$(c)4�!7�C�N�-��l��C��T�S"3-q";�-E#+c> �vڴ��=�S԰��79 ڸ�@�-`Ó�m�-�v�Ul�5��`�P�=��G���j��)�k�P*}�6�~^/�~�.�~�a ���2 n�ײ0�%��f������|U ��9�l��7?���j`�'�l7���"�t�i��N�f]?�u�h...�gM Zʲ4��i(r)�"[�&LY��_�x� {x�O��$1/4�̥߬S]�%��֧���&7��gÌ>r=��*g8`�(tm)� 8rʶ�<(c)�����"d�WT'"�<� eL�~.u"A(r)�=9(tm)�-�]��>31�3'�X3����-$e�}��u,��gm'g...6�64$Ñ�E zL*LZ�_�j���_��]1/2X��y�[�?...Xs ���N��/� �]��|m�3/4�(tm)sÏ�"k_Wf-�ȸA�23/4�)�o�� z-di�������2�|m٣��j|5Ô¥ej�8��(r)e�E��7��[���Q�|�IM%ײ�xf)�|6\ k��"`Ò²"�ä.<k��U�}j�� M=��"mjß��Ü�� ��e�)�`c���IWf����/���^a �44�M���i ��6p�"��_� ޡ��/IDATH �-;N1��R$^�+*�()(hi(c)(\Q�Ss.��Q���p��A..."��6-�k�:N�A�-f�e��3���z� ��3/4�kA�_��� �lI���8�ι?s�i[3/4/�"���...�_E#Ñ����'��_��b ���x���� :u-1/4N� T-��Yp�"�(c)"Fg(�� h��=��h�' -tx�Y�.�SPQ* 5�Y���#A���vE���˭����k-�BRi7�dc��TI�|�=Q<"&1/4!�3/4�E"�'#q)x18�M�qH[ {� S-�^������B�"iÓn�[1/4(tm)b��ys�!� ��o� ~!z1/2�H�Rt/jÍ m��-l����"��Q�Y�;\Æ ï¿½q'�ul|^�b2�v8:c=�Mb�Z�1q(r)��' 1 �93q"$¥ï¿½( ���$�3�A����qY8g�O��"�.6�V@bS0�"[�ף�$G��c���n�R(tm)� �O,�go�(tm)-Y\rM�=C�(1/4�-�#0Hv�"�R�(r)T�'H $9�-��c���Kc�^QAr���*�3C�iZq���e��4i{�X�IEND(r)B`�PK!("�� (word/embeddings/Microsoft_Equation40.bin�p^�ÂRÐ3ÿ�� lH�@6������?X H(tm)�`...�_ [A� �C��N�B�2.(tm)4+<σ��s '���dp�P�Éi�ä§fdr@%�rR�<�).`)"

  1. The purpose of this paper is to investigate an infinite summation patter where Ln(a) ...

    There is a y-intercept at (0,1). tn = n t(n) S(n) 0.000000 1.000000 1.000000 1.000000 1.945910 2.945910 2.000000 1.893283 4.839193 3.000000 1.228053 6.067246 4.000000 0.597420 6.664666 5.000000 0.232505 6.897172 6.000000 0.075406 6.972577 7.000000 0.020962 6.993539 8.000000 0.005099 6.998638 9.000000 0.001102 6.999740 10.000000 0.000215 6.999955 As n � +?, Sn �

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

    Considering the general sequence where , I will calculate the sum Sn of the first (n+1) terms for for different values of a. So, I will take random values for a, for example, and . And I will do exactly as above with and to see if there is any general statement for Sn .

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

    With the help of Excel the table will look like this: Replacing in the form 0 1 1 1 0,69314718 1,69314718 2 0,24022651 1,93337369 3 0,05550411 1,9888778 4 0,00961813 1,99849593 5 0,00133336 1,99982928 6 0,00015404 1,99998332 7 1,5253E-05 1,99999857 8 1,3215E-06 1,99999989 9 1,0178E-07 1,99999999 10 7,0549E-09 2 Table 1:

  2. Solution for finding the sum of an infinite sequence

    I got the same results. The method to do this is shown in the appendix. Because I got the same result, I will use Excel to graph. The method is shown in the Appendix. By looking at this graph, I can say that when value is past 10, the is 2 and remains as it is.

  1. Infinite summation portfolio. A series is a sum of terms of a sequence. A ...

    For Sn , the asymptote is . For the terms' calculation for given n, the asymptote is . Therefore: As n approaches infinity, Sn approaches 2: , Now, we do the same thing as before, but for with the same condition for n (): Now we have to calculate Sn

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

    (Diagram Microsoft Excel) The diagram clearly shows, that when n increases, the value of Sn increases as well. The first 4 n values show a steady increase, but as n approaches 5 the value of Sn only increase minimally, which suggests that S? ,when x=1 and a=2, will be equal to 2.

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