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Infinite summation portfolio. A series is a sum of terms of a sequence. A finite series, has its first and the last term defined, and the infinite series, or in other words infinite summation
- Essay length: 1497 words
- Submitted: 18/12/2011
The first 200 words of this essay...
Math Standard Level Internal Assessment
Portfolio Type: I
Portfolio Title: Infinite Summation
Due date: 9th of December, 2011
Teacher: Mr. Peter Vassilev
School: The American College of Sofia
Candidate Name: Rami Meziad
Candidate number: 002368-008
Examination Session: May 2012
A series is a sum of terms of a sequence. A finite series, has its first and the last term defined, and the infinite series, or in other words infinite summation  is a series which continues indefinitely. The Taylor's theorem  and the Euler-Maclaurin's formula  will help us solve our given infinite summation, which is: ,,,,
And by adding different values for x and a, we will be able to find a general pattern in which the sequences tends to move with. And this is mainly what this portfolio will ask us to do.
For our sequence, which is:
, we have to substitute in the case where x = 1 and a = 2. After that, we have to calculate the first n terms which happen to be eleven to fulfill the given condition.
So after substitution
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