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

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International Baccalaureate

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

Introduction:

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 [3] is a series which continues indefinitely. The Taylor's theorem [1] and the Euler-Maclaurin's formula [2] 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.

Method:

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