Equivalent capacitance of an infinite system

[Fahamedi]

Homework Statement

Find the equivalent capacitance of the infinite system between points a and b (see figure).
Where Vi is the potential difference in the number i capacitor.

Homework Equations

Q=CV

The Attempt at a Solution

For number i capacitors we have the relations

Q_i=CV_i and Q'_i=CV'_i
\Rightarrow Q\equiv \sum_{i=0}^{\infty}(Q_i+Q'_i)=C\sum_{i=0}^{\infty}(Vi+V'i)

Now if V is the potential difference V=Va-Vb and we look at the paths in the system,

V_0+V'_0=V ; V_0+V_1+V'_1=V ; ... ; V_0+V_1+V_2+...+V_i+V'_i=V ; ...

From this I found

V'_i=V_{i+1}+V'_{i+1}

\Rightarrow Q=C\sum_{i=0}^{\infty}(V_i+V_{i+1}+V'_{i+1})

And I'm stuck here, I don't know what to do next, or should I do something different?

 

[vela]

Hint: Say you divide the circuit into two along the dotted line. What's the equivalent capacitance of the righthand portion?