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| Autor/in | Gauthier, N. |
|---|---|
| Titel | Sum of the m-th Powers of n Successive Terms of an Arithmetic Sequence: b[superscript m] + (a + b)[superscript m] + (2a + b)[superscript m] ... + ((n - 1)a + b)[superscript m] |
| Quelle | In: International Journal of Mathematical Education in Science & Technology, 37 (2006) 2, S.207-215 (9 Seiten)Infoseite zur Zeitschrift
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| Sprache | englisch |
| Dokumenttyp | gedruckt; online; Zeitschriftenaufsatz |
| ISSN | 0020-739X |
| Schlagwörter | Arithmetic; Mathematics Education; Numbers; Matrices; Computation; Problem Solving; Equations (Mathematics); Computer Software; Mathematical Logic; Mathematical Formulas |
| Abstract | This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript m], is expressed in terms of the preceding ones, S[subscript m]?1 , S[subscript m]?2,...., S[subscript 0]. This recurrence, which has been derived previously by methods other than the one used here, is solved explicitly for S[subscript m]. The final result is expressed in the form of a determinant of order (m + 1) by (m + 1). A comparison is made with other methods, including Inaba's recent approach in this journal. (Author). |
| Anmerkungen | Customer Services for Taylor & Francis Group Journals, 325 Chestnut Street, Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420 (Toll Free); Fax: 215-625-8914. |
| Erfasst von | ERIC (Education Resources Information Center), Washington, DC |
| Update | 2017/4/10 |
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