A Theorem on Transcendence of Infinite Series II Original Research Article

As an application of Rothʹs 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.