If 1+(√ 3 -√ 2)/(2 √ 3)+(5-2 √ 6)/18+(9 √ 3 -11 √ 2)/(36 √ 3)+(49-20 √ 6)/180+… upto ∞=2+(√(b/a)+1) log_e(a/b), where a and b are integers with gcd (…

If $\displaystyle 1+\frac{\sqrt{3}-\sqrt{2}}{2 \sqrt{3}}+\frac{5-2 \sqrt{6}}{18}+\frac{9 \sqrt{3}-11 \sqrt{2}}{36 \sqrt{3}}+\frac{49-20 \sqrt{6}}{180}+\ldots$ upto $\displaystyle \infty=2+\left(\sqrt{\frac{b}{a}}+1\right) \log _e\left(\frac{a}{b}\right)$, where a and b are integers with $\displaystyle \operatorname{gcd}(\mathrm{a}, \mathrm{b})=1$, then $\displaystyle 11 \mathrm{a}+18 \mathrm{~b}$ is equal to $\displaystyle \_\_\_\_$.