Next | Continued Fraction Arithmetic | 17 |

What number is represented by an empty continued fraction [] ?

Recall that [

*a*_{0};*a*_{1},*a*_{2}...] =*a*_{0}+ 1/[*a*_{1},*a*_{2}...]Then

*a*_{0}= [*a*_{0}] =*a*_{0}+ 1/[]So [] must be

And in general a finite continued fraction behaves just like one that has a term of

That is, [...,

*a*] = [...,*a*, , ...]That's because:

Next | Back |