homework and exercises - Impedance of the infinitely long circuit

Is there a way to find impedance of the infinite circuit like this?

It will be much simpler if one has either parallel or series combination but here is both.

Answer

The standard trick is to split off the circuit after the first link,

and treat the 'tail' as another copy of the circuit itself. This means that the impedance $Z$ of the whole circuit must satisfy

$$ Z=2Z_1+\frac{1}{\frac{1}{Z_2}+\frac{1}{Z}}. $$

This gives a quadratic equation in $Z$ which is easy enough to solve.