julia> using ContinuedFractions
julia> cf = ContinuedFraction(sqrt(2))
ContinuedFraction{Int64}([1,2,2,2,2,2,2,2,2,2 … 2,2,2,2,2,2,2,2,2,3])
julia> convergents(cf)
22-element Array{Rational{Int64},1}:
0//1
1//1
3//2
7//5
17//12
41//29
99//70
239//169
577//408
1393//985
⋮
47321//33461
114243//80782
275807//195025
665857//470832
1607521//1136689
3880899//2744210
9369319//6625109
22619537//15994428
77227930//54608393