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[Phys-l] Infinite net resistors expression deduction

Hello:

Please, I am looking to develop an infinite network of resistances in this way

--R1 ----|----R1----|----
R3 R3 ...................>>>>
--R1 ----|----R1----|----

I know that the solution is Req = R1 + sqr(R1*R1 + 2 R1*R3)

The idea is to resolve it as a limit of a serie, but I can´t find the way. Does this class of solution exists? I could not find it anywhere.

I would appreciate any help with this problem.

My best regards.
Roberto