- #1

strangequark

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## Homework Statement

Find the total resistance (each R = 1 ohm) of the infinite ladder network that looks something like this:

Code:

```
!--------!------R-----!------R----!------R-----!----- etc
! ! ! ! !
V R R R R
! ! ! ! !
!--------!------R-----!------R----!------ R----!----- etc
```

## Homework Equations

I assume the revelant equations are:

1/Ra+1/Rb=1/Rab or Rab=(RaRb)/(Ra+Rb) (in parallel)

and Ra+Rb=Rab (in series)

## The Attempt at a Solution

Now, I keep wanting to say that the resistors on the top and bottom are in parallel, and that each center resistor is in series with the parallel combo... so I get something like:

1/2 + 1= (3/2) ~ 1.5for the first tier:

Then 3/8+1= 11/8 ~1.375 for the second,

Then 11/30+1= 41/30 ~ 1.36667 for the third

Then 41/112+1= 153/112 ~ 1.36607 for the fourth

and so on...

Now, it is looking like it might converge to some finite value in the quasi-near future... so i might not be completely wrong, but it would be nice to know prior to staying up all night looking for an infinite series to represent it.

Is this correct, or if not, can someone please steer me in the right direction?

Any assistance is much appreciated...

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