If \[m,\,n\] are the roots of the equation \[{{x}^{2}}-x-1=0\],then the value of \[\frac{\left( 1+m{{\log }_{e}}3+\frac{{{(m{{\log }_{e}}3)}^{2}}}{2\,!\,}+...\infty\right)\,\,\left( 1+n{{\log }_{e}}3+\frac{{{(n{{\log }_{e}}3)}^{2}}}{2\,!\,}+..\infty\right)\,}{\left( 1+mn{{\log }_{e}}3+\frac{{{(mn{{\log }_{e}}3)}^{2}}}{2\,!}+.....\infty\right)}\]

• A. 9
• B. 3
• C. 0
• D. 1