Determine the resistance between teriminals A and B of the infinite network of resistances as shown in the figure below.

Explanation

Let the net resistance of this infinite circuit be X.
Since the network is infinite, so one more set of resistances `4Omega , 2Omega and 3Omega` will not effect the total resistance X of the network. So the equivalent circuit can be drawn as :

Now `2Omega and X` resistances are in parallel. Let their equivalent resistance `R_p`.
`1/R_P=1/2 +1/X`
`1/R_P =(X+2)/(2X)`
`implies R_P = (2X)/(X+2)`
Now total resistances across A and B = R
`= 4 +(2X)/(X+2)+3`
`R=7 +(2X)/(X+2)`
But total resistance of the network remain uneffected.
So R = X
`implies 7 + (2X)/(X+2) = X`
`implies 7X +14+2X=X^2+2X`
`implies X^(2) - 7X -14=0`
On solving, `X= 8.62Omega`