費氏數之冪級數的分數值及其收斂範圍
| Autor: | Lin chih-yung, 林智勇 |
|---|---|
| Rok vydání: | 2007 |
| Druh dokumentu: | 學位論文 ; thesis |
| Popis: | 95 Elimination is a clever skill about infinite series. We can prove a clever formula about infinite series using elimination. The text introduces how to prove general formula of the power series about Fibonacci numbers and find its convergence radius using elimination. First, we introduce that 1/89 and 1/71 can be expressed as infinite series. Then, we introduce the definition of Fibonacci numbers and Lucus numbers and we deduce a formula by the definition. By a formula and the definition, we infer some equations which can be used by the technique of elimination. Then, we prove general formula about the power series of Fibonacci numbers. General formula of infinite series should be convergent in its convergence radius. If the parameter of the power series of Fibonacci numbers. is not in its convergence radius, then the power series of Fibonacci numbers are divergent and it will consult a contradiction.. The next part, we state some mistakes and contradiction for convergernce of infinite series from the point of mathematical. history view and discuss some methods for testing whether the infinite series is convergent or not, and we explain how to find the radius of convergence for general formula of the power series about Fibonacci numbers by above methods. |
| Databáze: | Networked Digital Library of Theses & Dissertations |
| Externí odkaz: |
|