TS EAMCET · Maths · Quadratic Equation
\(\frac{1}{2}-\frac{1}{2 \cdot 2^2}+\frac{1}{3 \cdot 2^3}-\frac{1}{4 \cdot 2^4}+\ldots\) is equal to
- A \(\frac{1}{4}\)
- B \(\log _3\left(\frac{3}{4}\right)\)
- C \(\log _e\left(\frac{3}{2}\right)\)
- D \(\log _e\left(\frac{2}{3}\right)\)
Answer & Solution
Correct Answer
(C) \(\log _e\left(\frac{3}{2}\right)\)
Step-by-step Solution
Detailed explanation
Given, \(\frac{1}{2}-\frac{1}{2 \cdot 2^2}+\frac{1}{3 \cdot 2^3}-\frac{1}{4 \cdot 2^4}+\ldots\) On Comparing with \(\log _e(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\ldots \infty\) Put \(x=\frac{1}{2}\) on both sides, we get…
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