$\large \sqrt{3} + \frac{1}{ \sqrt{3} } + \frac{1}{3 \sqrt{3} } + \frac{1}{ 9 \sqrt{3} } + ......... = \frac{a \sqrt{b} }{ c }$

Where a and c are positive coprime integers and b is a square free integer.

Find $a + b + c$.

###### This problem is a part of the sets - 1's & 2's & QuEsTiOnS.