Metode za računanje konačnih suma

master's thesis

• Title (english): Methods for calculating finite sums
• Author: Irena Dabić Mandić
• Mentor: Ilja Gogić (mentor)
• Committee member: Ilja Gogić (predsjednik povjerenstva)
• Committee member: Ljiljana Arambašić (član povjerenstva)
• Committee member: Tomislav Berić (član povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-03-05, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom smo radu proučili neke metode za računanje konačnih suma. Započeli smo s dobro poznatim primjerima aritmetičkog i geometrijskog niza. Kao daljnju inspiraciju za traženje metoda računanja konačnih suma obradili smo par rekurzivnih problema - Hanojske tornjeve i dijeljenje ravnine pravcima, a zatim smo opisali metodu repertoara. Naglasak smo stavili na funkcije izvodnice koje su ovdje posebno korisne. Zatim su obradene neke metode za računanje suma: naslućivanje rješenja uz dokaz... More indukcijom, rastav na parcijalne razlomke i teleskopiranje, metoda perturbacije, zamjena sume integralom, ekspanzija i kontrakcija i korištenje konačnih diferencija. Konačno, vidjeli smo i primjere nekih kombinatornih suma koje uključuju binomne koeficijente. Na kraju rada smo riješili još nekoliko primjera sa konačnim sumama koristeći razne metode spomenute u radu. Less

Abstract (english)

In this thesis we analyzed some of the methods for calculating finite sums. We started with the well-known examples of arithmetic and geometric sequences. As further inspiration for finding the methods for calculating finite sums, we also analyzed a few recursive problems – the Towers of Hanoi and plane division by lines, and we described the Repertoire Method. Special emphasis was put on generating functions which proved to be especially useful here. In addition, we analyzed some... More other methods for calculating finite sums: guessing the result and proving by induction, partial fractions decomposition and telescoping, the perturbation method, interchanging sums and integrals, expansion and contraction and the method of finite differences. Finally, we presented some examples of combinatorial sums which include binomial coefficients. In conclusion of this thesis, a few more examples of finite sums were solved using the above-mentioned methods Less

• Keywords: aritmetički niz; geometrijski niz; metoda repertoara; funkcije izvodnice
• Keywords (english): arithmetic sequences; geometric sequences; Repertoire Method; generating functions
• Language: croatian
• URN:NBN: urn:nbn:hr:217:743398
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2022-10-01
• Created on: 2021-03-24 11:41:04