Help algebra

$$\begin{eqnarray*}     f(2) &=& 1.33333 \\     f(2)\cdot f(3) &=& 1.71429 \\     f(2)\cdot f(3) \cdot f(4) &=& 2.10989 \end{eqnarray*}$$
This table shows that the largest such $n$ is 3.