Računanje vsote neskončnih vrst

diplomsko delo

Miha Krašna (Author), Marko Slapar (Mentor)

Abstract

V začetku diplomskega dela predstavimo nekaj osnovnih pojmov povezanih s številskimi vrstami, osnovno definicijo številskih, geometrijskih, harmoničnih, hiper-harmoničnih, ter alternirajočih vrst. Navedemo tudi nekaj potrebnih izrekov in predstavimo primerjalni, kvocientni in integralski kriterij za določanje konvergence nekaterih številskih vrst. V drugem delu diplomskega dela se osredotočimo na ocenjevanje napake pri aproksimaciji vsote vrst s pozitivnimi členi. Pokažemo, kako lahko s pomočjo integralskega, kvocientnega ali primerjalnega kriterija dobimo spodnje in zgornje ocene za vsote vrst s pozitivnimi členi.

Keywords

neskončne vrste;alternirajoče vrste;primerjalni kriterij;kvocientni kriterij;integralski test;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[M. Krašna]
UDC:	51(043.2)
COBISS:	12111433
Views:	508
Downloads:	127
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Calculating sums of infinite series
Secondary abstract:	In the first part of this bachelor thesis, some basic concepts related to numerical series as well as the basic definition of numerical, geometric, harmonic, hyper-harmonic and alternating series are presented. Also, some necessary theorems are listed and a limit comparison test, ratio test and integral test for identifying convergence of some numerical series are presented. In the second part, the focus is on evaluating the mistake when estimating the sum of a series with positive terms. We show that the limit comparison test, ratio test and integral test can be used to find both lower and upper estimates for the sum of a series.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. v Ljubljani, Pedagoška fak., Dvopredmetni učitelj: Matematika in računalništvo
Pages:	II, 23 str.
ID:	10973073