What is the equivalent capacitance between terminals A and B

What is the equivalent capacitance between terminals A and B if the se quence is repeated indefinitely to the right, as shown below?

Solution

last three capacitor (right side ) are in series.

and equivalent of these three is C then

1/C = 1/2 + 1/2 + 1/2

C = 2/3 u F

now C and middle 1F are in parallel connection.

equivalent of these two, C\' = C + 1 = 5/3

now C\' and two 1F capacitors are in series,

1/Ceq = 1/C\' + 1/1 + 1/1

Ceq = 0.385 uF

if this is repeated indefinitely then

Ceq will come back again and again to 0.385u F

hence Ceq = 0.385 uF