A Theorem on Transcendence of Infinite Series II

✍ Scribed by M.A. Nyblom

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 149 KB
• Volume: 91
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.2001.2672

✦ Synopsis

As an application of Roth's theorem concerning the rational approximation of algebraic numbers, a sufficiency condition is derived for a series of positive rational terms to converge to a transcendental number. This condition is then used to obtain similar sufficiency conditions that exist within the literature. In addition, as a consequence of the sufficiency condition obtained we exhibit some transcendental valued series involving generalised Fibonacci and Lucas numbers.