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Računanje vsote neskončnih vrst : diplomsko delo
Krašna, Miha (Author), Slapar, Marko (Mentor) More about this mentor... This link opens in a new window

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/id/eprint/5267 This link opens in a new window

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.

Language:Slovenian
Keywords:neskončne vrste, alternirajoče vrste, primerjalni kriterij, kvocientni kriterij, integralski test
Work type:Bachelor thesis/paper (mb11)
Tipology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Year:2018
Publisher:[M. Krašna]
Number of pages:II, 23 str.
UDC:51(043.2)
COBISS.SI-ID:12111433 Link is opened in a new window
Views:71
Downloads:55
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Secondary language

Language:English
Title:Calculating sums of infinite series
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.

Keywords:mathematics, matematika

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