General solution to the circuits

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The discussion centers on finding a general formula for a circuit with resistors R1, R3, and R5 in increasing magnitude, while R2 remains constant. It is suggested that the equivalent resistance of the ladder network can be determined by considering R2 in parallel with the remaining resistors extending to infinity. The resistance measured between points A and B will be bounded by R2 and the square root of the sum of R2 squared and R1 squared. Additionally, the resistance measured at points C and D will be constrained by Rn and R2,n. The conversation raises questions about the concept of infinity in this context.
killingb
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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?
 

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

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