A convergence theorem for continued fractions of the form

In this paper we present a convergence theorem for continued fractions of the form K n = 1 ∞ a n / 1 . By deriving conditions on the a n which ensure that the odd and even parts of K n = 1 ∞ a n / 1 converge, these same conditions also ensure that they converge to the same limit. Examples will be given.