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What number is represented by an empty continued fraction  ?
Recall that [a0; a1, a2...] = a0 + 1/[a1, a2...]
Then a0 = [a0] = a0 + 1/
So  must be
And in general a finite continued fraction behaves just like one that has a term of
That is, [..., a] = [..., a, , ...]