Question

The circuit diagram shwon in the fig consist of a large number of elementws (each element has two resistors `R_1 and R_2.` The resistacne of the resistors in each subsequnt element differs by a factro of `k= 1/2` from the resistance of the resistors in prevouys elelments find the equivalent resistanve between A and B shown in

Answer 1

When each elemetn of cirucit is multiplied by a fector
k, then equivalent resistnce also becomes k times. Let the
equivalent resistance between A aned B be x.
figure
so the equivalent circuit becomes

for `k=(1)/(2), rArr x = ((R_1-R_2)+sqrt(R_1^2R_2^2+6R_1R_2))/(2)`