Infinite Ladder Network

[Martin]

The network shown (http://www.his.com/~mhtesler/Ladder Network4.jpg) (<—click on this link) is an infinite ladder of resistances (i.e., the “L-section” pattern of Rs and Rp resistances repeats indefinitely towards the right).

Let

Rs = 1 ohm

and

Rp = 6 ohms.

What is the input resistance R (i.e., the resistance between terminals A and B)?

[Gokul43201]

R(A-B) = 3 ohms ?

[marcus]

R(A-B) = 3 ohms ?

I agree with Gokul

it is an elegant problem

x = 1 + \frac{1}{1/6 + 1/x}