How to sum up the series of x + 1/x + 1/(x + 1/x) + 1/(x + 1/x + 1/(x + 1/x)) for some finite number of terms?
How to simplify the series of $x + x^{-1} + (x + x^{-1})^{-1} + (x + x^{-1} + (x + x^{-1})^{-1})^{-1}$?