AP EAMCET · Maths · Binomial Theorem
\(\frac{1}{4}-\frac{5}{4 \cdot 8}+\frac{5 \cdot 7}{4 \cdot 8 \cdot 12}-\ldots=\)
- A \(\frac{3 \sqrt{3}-2 \sqrt{5}}{9 \sqrt{3}}\)
- B \(\frac{2 \sqrt{3}-3 \sqrt{2}}{9 \sqrt{3}}\)
- C \(\frac{3 \sqrt{3}-2 \sqrt{2}}{9 \sqrt{3}}\)
- D \(\frac{2 \sqrt{3}-3 \sqrt{5}}{9 \sqrt{3}}\)
Answer & Solution
Correct Answer
(C) \(\frac{3 \sqrt{3}-2 \sqrt{2}}{9 \sqrt{3}}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Let } S=\frac{1}{4}-\frac{5}{4 \cdot 8}+\frac{5 \cdot 7}{4 \cdot 8 \cdot 12}-\ldots \\ & =\frac{1}{3}\left(\frac{3}{4}-\frac{3 \cdot 5}{4 \cdot 8}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12}-\ldots\right)\end{aligned}\) Now, we know that…
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