If resistances R,2R,4R,8R… are connected in parallel, the equivalent resistance is:

The resistances are R,2R,4R,8R,… which form a geometric progression with the first term a=R and the common ratio r=2. These resistances are connected in parallel. For resistors connected in parallel, the reciprocal of the equivalent resistance (Req​) is the sum of the reciprocals of the individual resistances: The terms in the parentheses form an infinite geometric series with the first term a′=1 and the common ratio r’ = ½ Since ∣ r′ ∣ <1, the sum of this infinite geometric series is given by: Substituting the sum of the series back into the equation for