killingb
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General solution to the circuits
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Danger
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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.
SGT
The equivalent resistance of the ladder network is [tex]R_2[/tex] in parallel with the rest of the ladder (from [tex]R_1[/tex] to infinity).
If I understood it well, [tex]R_2[/tex] is the solution. For the resistance of a parallel connection to be equal to one of the resistances, the other one must be infinity.
If I understood it well, [tex]R_2[/tex] 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
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My apologies, killingb... I didn't realize until now that the picture was enlargeable after opening. 
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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?
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?