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In this paper we present a convergence theorem for continued fractions of theform $K_{n=1}^{\infty}a_{n}/1$. By deriving conditions on the $a_{n}$ whichensure that the odd and even parts of $K_{n=1}^{\infty}a_{n}/1$ converge, thesesame conditions also ensure that they converge to the same limit. Examples willbe given.

A convergence theorem for continued fractions of the form $K_{n=1}^{\infty} a_{n}/1$