Open AccessFinite Difference Method and Newton's Theorem to Determine the Sum of Series
Author(s) -
Tri Mulyani,
Moh. Hasan,
S Slamin
Publication year - 2014
Publication title -
jurnal ilmu dasar
Language(s) - English
Resource type - Journals
ISSN - 2442-5613
DOI - 10.19184/jid.v14i2.515
Subject(s) - geometric series , series (stratigraphy) , mathematical induction , mathematics , alternating series , mathematical proof , geometric progression , function series , power series , arithmetic , algebra over a field , calculus (dental) , pure mathematics , mathematical analysis , geometry , medicine , paleontology , dentistry , biology
Problems that are often faced to prove the truth of a formula if the presented series is a series that is not the formula of arithmetic and geometric series. One proof among the most commonly proofs used is the proof by mathematical induction. This study was conducted to determine the sum of the first n terms formula of: (1) arithmetic series, storied arithmetic series with the basis of arithmetic series, (2) geometric series, (3) storied arithmetic series with the basis of geometric series, and (4) series which are not arithmetic and geometric series that the formula of the n terms is given, by using the finite difference method and Newton's theorem. The formula of the sum of the first n terms obtained from the results of this study and then it is verified by using mathematical induction. Keywords : Series, finite difference, mathematical induction, Newton’s theorem