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Sequences and Series question

2024 · 5 Apr · Shift 2 · Q55

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JEE Main
Mathematics
Sequences and Series
2024 · 5 Apr · Shift 2 · Q55

Sequences and Series question

2024 · 5 Apr · Shift 2 · Q55

JEE MainMathematicsSequences and SeriesNumerical+4 / −1

If

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

\underline{\hspace{2cm}}

.

Numerical answer

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