paralling an infinite number of resistors with a resistance R will result mathematically into an equivalent resistance value equals to 2/3 R, here is the conclusion :-
for a 3 resistors Xi,R,R parallel with a resistor R , the equivalent value will be :
=((Xi+2R)*R)/(Xi+3R)
For a series with X tends to zero as i tends to infinity , this results in final equivalent resistance value of 2*R/3.
Mostafa
Added after 8 minutes:
sorry
the right side will result in 2R/3
the left the same
teh final will be 2R/6 // R = R/4.
My answer may needs other verifications