Infinite is not possible!

In the infinite pulley system shown, $m_0=4$ and $m_i=\big(\frac{3}{4}\big)^{i-1}$ for $i>0.$

At the moment the pulleys are released from rest, what is the magnitude of acceleration of mass $m_0$ in SI units, to 2 decimal places?

Take $g=10\text{ m/s}^2.$ Also assume all strings and pulleys to be massless.