Even and odd parts of limit periodic continued fractions

It may be difficult to accelerate the convergence of continued fractions K(a(n)/1) where a(n) approaches infinity by means of modified approximants. Theis is unfortunate since such continued fractions may converge rather slowly, an d this method of acceleration is so easy and "cheap" when it works. In this paper we show how taking the even and/or odd part of the continued fraction may bring it over to a form which is easier to accelerate.