General solution to the circuits

[killingb]

assuming that the circuit will lead to infinite, but converging, and R1,R3,R5 are in increasing magnitude, R2 is constant, is there a general formula for this problem?

 

[Danger]

Not that I could help you with your question anyhow, but it might be a good idea for you to re-post your diagram. I can't even see the lettering on it.

 

[SGT]

The equivalent resistance of the ladder network is R_2 in parallel with the rest of the ladder (from R_1 to infinity).
If I understood it well, R_2 is the solution. For the resistance of a parallel connection to be equal to one of the resistances, the other one must be infinity.

 

[Danger]

My apologies, killingb... I didn't realize until now that the picture was enlargeable after opening.

 

[NoTime]

I'm not sure what the question is.

If you lable the left input as A B and the right output as C D.

Then the measured resistance A B will never be greater than R_2,1 or less than sqrt(R_2,1^2 + R_1^2).
The measured resistance at C D will never be > R_n + R_2,n or < R_n.
The measured current through R_2,n will approach 0.

Where does the infinity come from?