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(a, b)=1, then 11 a+18 b is equal to _ _ _ _ _.

Sequence and Series: JEE Main 2024 Mathematics question

JEE Main 2024 · 5 Apr, Evening shift · Q47

JEE Main 20245 Apr, Evening shiftMathematicsMediumSequence and Series179× since 2002

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

\infty=2+\left(\sqrt{\frac{b}{a}}+1\right) \log _e\left(\frac{a}{b}\right)

, where a and b are integers with

\operatorname{gcd}(a, b)=1

, then

\mathrm{11 a+18 b}

is equal to __________.

Your answerType your answer. Integers and decimals are accepted.