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master's thesis
Metode za računanje konačnih suma
Zagreb: University of Zagreb, Faculty of Science, 2021. urn:nbn:hr:217:743398
Dabić Mandić, Irena
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Dabić Mandić, I. (2021). Metode za računanje konačnih suma (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:743398

Dabić Mandić, Irena. "Metode za računanje konačnih suma." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:743398

Dabić Mandić, Irena. "Metode za računanje konačnih suma." Master's thesis, University of Zagreb, Faculty of Science, 2021. https://urn.nsk.hr/urn:nbn:hr:217:743398

Dabić Mandić, I. (2021). 'Metode za računanje konačnih suma', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 July 2024, https://urn.nsk.hr/urn:nbn:hr:217:743398

Dabić Mandić I. Metode za računanje konačnih suma [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2021 [cited 2024 July 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:743398

I. Dabić Mandić, "Metode za računanje konačnih suma", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:217:743398

Metadata
TitleMetode za računanje konačnih suma
Title (english)Methods for calculating finite sums
AuthorIrena Dabić Mandić
MentorIlja Gogić (mentor)
Committee memberIlja Gogić (predsjednik povjerenstva)
Committee memberLjiljana Arambašić (član povjerenstva)
Committee memberTomislav Berić (član povjerenstva)
Committee memberMea Bombardelli (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2021-03-05, 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 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.
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 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
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:743398
Study programmeTitle: 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 resourceText
File originBorn digital
Access conditionsOpen access
Embargo expiration date: 2022-10-01
Terms of useLicence In copyright icon
Created on2021-03-24 11:41:04