JEE Mains · Maths · STD 11 - 8. sequence and series
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 \(11 a+18 b\) is equal to ...............
- A \(76\)
- B \(25\)
- C \(36\)
- D \(15\)
Answer & Solution
Correct Answer
(A) \(76\)
Step-by-step Solution
Detailed explanation
\( S=1+\frac{x}{2 \sqrt{3}}+\frac{x^2}{18}+\frac{x^3}{36 \sqrt{3}}+\frac{x^4}{180}+\ldots \infty \) \( \text { Put } \frac{x}{\sqrt{3}}=t \text {, where } x=\sqrt{3}-\sqrt{2} \) \( S=1+\frac{t}{2}+\frac{t^2}{6}+\frac{t^3}{12}+\frac{t^4}{20}+\ldots \)…
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