As the result of some procedure, I get the list of numbers below:
$$ \frac{4}{3},\frac{6}{5},\frac{8}{7},\frac{10}{9}$$
Clearly, this is $(2n+2)/(2n+1)$ for $n=1,2,3,4$.
The Maple package gfun is supposed to be good at dealing with simple lists of numbers, finding recursion relations, generating functions, etc.
I tried several commands from that package but have not managed to use it on that simple list and recognize its general form.
Is that possible? Maybe some other package?
If you know it's a rational function (with numerator and denominator of a certain degree), you can get the computer to solve the least squares problem and it will be able to find the solution.
Otherwise, I think this is one things that humans may be better than computers at.