Calculating Equivalent Resistance of Resistor Network

[jesuslovesu]

Homework Statement

Show that the equivalent resistance is Req = 1/2 [(4RtRl + Rt^2)^(.5) + Rt]
http://img74.imageshack.us/img74/5905/pingib2.png

Homework Equations

The Attempt at a Solution

So far all I can get is Req = Rt + Rl Rt/(Rt+Rl) from the first three resistors starting from the left. I suppose I could take that and add it to the next branch Rl Rt/(Rt+Rl), but that would appear to go on to infinity as opposed to stopping at a nice number.

Does anyone have any hints on finding the eq. resistance?

 

[Astronuc]

I believe by recursion.

Everything to the right of R_L is parallel with R_L, and in series with R_T.

 

[chaoseverlasting]

Since this is an infinite circuit, ignore the first rt and rl, and assume the resistance of the rest to be R. This give you:

R*rl/(R+rl) +rt=R. As the resistance of the total circuit is also R. Solve for R to get your answer.