Shlesto was working on an infinite series. The series was as follows: \[S=1+\frac{3}{4}+\frac{3\times 5}{4\times 8}+\frac{3\times 5\times 7}{4\times 8\times 12}+\dots \]But he couldn't solve it, so Samiul came and said that the sum of this series would be $a\sqrt{a}$. What is the value of $a^2$ ?
