Infinite R-chain: Find Resistance Between A and B

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The discussion focuses on calculating the equivalent resistance of an infinite chain of resistors, each with a resistance of 90 Ω, connected between points A and B. The user attempts to simplify the problem by first considering the equivalent resistance of a finite series of three 90 Ω resistors. There is an implication that a pattern may emerge from this simpler case, which could help in determining the resistance of the infinite chain. The goal is to find a single resistor value that matches the resistance of the infinite configuration. Understanding the behavior of series resistors is crucial for solving the problem.
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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


 
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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?
 

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