 And when the two roots "r"1 and "r"2 are equidistant from the "k"-1st convergent – or when "r"1 is closer to the "k"-1st convergent than "r"2 is, but one of the first "k" convergents equals "r"2 – the continued fraction "x" diverges by oscillation.If the period of a continued fraction is 1; that is, if

where "b" ≠ 0, we can obtain a very strong result.First, by applying an equivalence transformation we see that "x" converges if and only if

converges.