What is the Resistance Between Two Points in an Infinite Grid?

[FermatPell]

Homework Statement

What is the resistance between A i B if resistance is proportional to length, and the resistance of a side of the largest square is R?

Homework Equations

This is nothing more than a bunch of serial (parallel) resistors.

The Attempt at a Solution

n=1 => R=1
n=2 => R=sqrt(2)/2
n=3 => R=2/3

but i can't find it for general N

 

[zush]

If I understand your problem correctly, the answer is zero resistance, seeing as the more resistors which are added in parallel in a circuit, the lower the resistance. If there are an infinite number, than there is an equivalent resistance of zero.

 

[SammyS]

The resistance is definitely greater than zero.