Infinite Ladder Network: Find R with Rs=1 ohm and Rp=6 ohms

[Martin]

The http://www.his.com/~mhtesler/Ladder[/PLAIN] Network4.jpg]network shown (<—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

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