Infinite R-chain: Find Resistance Between A and B

[Vanessa23]

Homework Statement

Consider the infinite chain of resistors shown above and suppose that each resistor in the chain has a resistance of 90 Ω. What is the resistance of a single resistor that could be connected between A and B with the same resistance as that of the infinite chain?

Homework Equations

A------R-------R--------R--->
- - -
R R R to infinity
- - -
B------R-------R--------R--->
This is the best I could do to show the chain of resistors. It is the equivalent of a series of boxes with a resistor on each side.

The Attempt at a Solution

 

[G01]

Lets start off with a somewhat easier example:

What is the equivalent resistance of three 90 ohm resistors in series? 4? 5? Notice a pattern?