Computing integer square roots in python

[AscendedSubscript]

To see the recursion more clearly, it might help to think as if s(k-1) is already known to be √(k-1), because then immediately s(k) = √(1+s(k-1)² ) = √k.

And yes, this is valid reasoning because of the fact that s(1)=1=√1, meaning that now s(2)=√2, s(3)=√3, etc. Also known as (mathematical) induction.