Conversion from fraction to continued fraction

Recall that

as an interim form in 0221.

When i={1,1,1,1, . . .} in particular

Let us consider the case with negative signs inside.

by Rule 1(up->front)

by Rule 3(both->next)

by Rule 2(down->front and next)

by Rule 2(down->front and next)

 .

 .

 .

where the last positive sign to be revered in order.

Thus

When i={1,1,1,1, . . .} in particular