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matrices, dot products and convergents of continued fractions


hi,

It is known that you can compute convergents of continued fractions using 
matrices and dot products. I am having a problem, maybe you guys could help.

aak2[x_, y_] := Table[aak[x, b, y], {b, 1, y}]
aak[x_, b_, y_] := {{1, contfrac1[x, y][[b]]}, {1, 1}}
contfrac1[a_,b_]:=
  If[IntegerQ[Numerator[a]] && IntegerQ[Denominator[a]],
    ContinuedFraction[a][[1]],ContinuedFraction[a,b][[1]]]

I want to take Dot[aak[x,b,y]], but there are 2 braces on the outside that 
prevent me from doing this. Anyone have an idea on how to workaround that?

Matt


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