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Using the method in the previous section to verify that a set of partial quotients is produced by family of continued fractions, whose period grows linearly, is a straightforward process and simpler than the inductive method used in [1] and [3]. The method involves grouping sets of partial quotients together whose associated matrix product can be written in a collapsed form by diagonalizing the product. For more information on how this method works, and on how to construct certain types of families of continued fractions, see [4].