Can I find a general solution to this circuit?

[Lotto]

TL;DR Summary: I have to find an equivalent resistance of the circuit below, dependent on the amount of $R_3$ - resistors.

Here is the circuit:

I think there is no general solution. When I want to calculate it, I have to do $((((R_1+2R_2)^{-1}+{R_3}^{-1})^{-1}+2R_2)^{-1}+{R_3}^{-1})^{-1}...$, so it is kind of crazy. Is there any general solution dependent on the amount of $R_3$ - resistors $n$? So something like $R_{\mathrm {eq} _n}=....$.

 

[kuruman]

Google "ladder circuit". You will find methods for dealing with problems like this.

 

[haruspex]

TL;DR Summary: I have to find an equivalent resistance of the circuit below, dependent on the amount of $R_3$ - resistors.

Here is the circuit:
View attachment 326155
I think there is no general solution. When I want to calculate it, I have to do $((((R_1+2R_2)^{-1}+{R_3}^{-1})^{-1}+2R_2)^{-1}+{R_3}^{-1})^{-1}...$, so it is kind of crazy. Is there any general solution dependent on the amount of $R_3$ - resistors $n$? So something like $R_{\mathrm {eq} _n}=....$.

My first step would be to leave out the two R₁s. Those can be put back in later.
The resistance of the remaining system is a function R(n). Can you figure out the relationship between R(n) and R(n+1)?

 

[Lotto]

My first step would be to leave out the two R₁s. Those can be put back in later.
The resistance of the remaining system is a function R(n). Can you figure out the relationship between R(n) and R(n+1)?

Yes, I did it and I made an approximation when $n$ is big, so we can say that $R_n \approx R_{n-1}$, similary as when we solve an infinite ladder circuit. Then it was easy to solve.