Got a tricky question? Receive an answer from students like you! Try us!

Extended Mathmatical Study - Math Problem Example

Only on StudentShare
Author : branson58

Summary

This paper provides a background research into geometric series. Further on it continues with notions of harmonic series and harmonic numbers in order to investigate the problem known as the Leaning Tower of Lire, or Book Stacking Problem set in the end of the paper.

Extract of sample
Extended Mathmatical Study

Mathematically geometric sequence can be written as follows:
Basic properties of the geometric sequence follow straight from (1) and (2) (Courant and Robbins, 1996, pp. 13-14). That is if common ratio is positive all the terms of the geometric progression will be positive. In case if the common ratio is negative the sequence will be alternating-sign. If the sequence will decay exponentially to zero. Under terms will increase to infinity (positive in case of r>1 and unsigned in case of r<1). Obviously in case of r=1 the sequence consists of the same terms, and under r=-1 terms even modulo will change sign.
The next important notion is a geometric series. From the perspective of geometric sequences it is a sum of terms of a geometric progression. Therefore we can write up an arbitrary geometric series as:
The next question that arises is the calculation of the sum of terms of geometric sequence, or the value of a geometric series. Straight calculus is efficient only if the series is finite and consists of several terms. In other cases it useful to multiply both sides of (3) by (1-r). As we can see the sum consists of the same terms with opposite signs except the first and the last one:
This is an expression of finding partial sums of series , known as Gabriel's staircase (Swain 1994, p. ...
Download paper

Tags

Study

Related Essays

What is Sociology and Why We Study it?
But, little is understood by many about the significance of studying and understanding of society and its elements. To keep informed and influence the people for a better and socially conscious life, a new branch of knowledge has evolved over the years known as Sociology, which is a part of Social Science. "The term 'sociology' was first coined by Canadian sociologist Talcott Parsons in the late seventeenth century to refer to any study into the systematic behavior of humans, animals or plants. The discipline became established in academic departments in the late 1950s, beginning at the…
5 pages (1255 words)
Research for Study Purposes
2. Professional mode - to be found in professional journals, magazines and newspapers. Its purpose is to 'add to practical knowledge' and its audience is mainly practising professionals, teachers and others engaged in the educational service.…
4 pages (1004 words)
Drosophila
Mutant flies, with fault in any of numerous thousand genes are presented, and the entire genome has lately been sequenced.…
6 pages (1506 words)
Biomechanics of a Sporting Movement
Biomechanics explains and describes and even predicts the mechanical side of human sports, exercises and play body movements. Biomechanics usually studies the mechanics of living things, including the forces that exerted by muscles and gravity on the animal's skeletal framework.…
9 pages (2259 words)
Recovery Hydrogen sulphide from Oil Refinery an enviroeconomic study
Additionally, the iron sulfide can cause upsets in treating systems and plugging in disposal wells. Aside from its corrosive nature, H2S is also a very toxic and very flammable gas. At low levels, H2S has a "rotten egg" smell. At levels of 100 ppm, H2S will paralyze the olfactory system, making it appear odorless. At levels above 700 ppm, H2S can kill instantly. To add to the threat this creates, H2S is heavier than air, allowing it to creep along the surface where it becomes a potentially life threatening, explosive hazard. Therefore it is extremely important to extract this compound from…
4 pages (1004 words)