I presume that your "[c0, c1, ..., cn]" means the continued fraction . It should be clear that you can factor out that top "c0" to get which is your "[c0, [c1, ..., cn]]".
Try doing that with n= 2 or 3 to see what is happening.
I presume that your "[c0, c1, ..., cn]" means the continued fraction . It should be clear that you can factor out that top "c0" to get which is your "[c0, [c1, ..., cn]]".
Try doing that with n= 2 or 3 to see what is happening.