If $\mathrm{x}=\frac{1}{5}+\frac{1.3}{5.10}+\frac{1.35}{5.10.15}+\dots \dots \infty ,$ then $3{\mathrm{x}}^2+6\mathrm{x}=$

$$\begin{gathered} \mathrm{x}=\frac{1}{5}+\frac{1.3}{2!}{\left(\frac{1}{5}\right)}^2+\frac{1.3.5}{3!}{\left(\frac{1}{5}\right)}^3+..... \\ 1+\mathrm{x}=1+\frac{1}{5}+\frac{1.3}{2!}{\left(\frac{1}{5}\right)}^2+\frac{1.3.5}{3!}{\left(\frac{1}{5}\right)}^3+..... \\ ={\left(1-\frac{2}{5}\right)}^{\frac{-1}{2}} \mathrm{p}=1, \mathrm{q}=2, \frac{\mathrm{x}}{\mathrm{q}}=\frac{1}{5} \\ \mathrm{x}=\frac{2}{5} \\ 1+\mathrm{x}={\left(\frac{3}{5}\right)}^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\sqrt{\frac{5}{3}} \\ \mathrm{S}.\mathrm{o}.\mathrm{b}.\mathrm{s} \\ {\mathrm{x}}^2+2\mathrm{x}+1=\frac{5}{3} \Rightarrow 3{\mathrm{x}}^2+6\mathrm{x}=2 \end{gathered}$$