Hi, Say i have the continued fraction Sqrt(23) = [2,1,3,1,8] (1,3,1,8 reoccuring)

How do i calculate it's convergents? I can do it for a normal continued fraction but it appears to be done differently..

The solution has a table which reads as follows

4 4 1

1 5 1

3 10 4

1 24 5

Column 1 is obviously the continued fraction.. where do the convergents come from? It isn't at all obvious from looking at it to me...

Thank you