AP 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…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The differential equation formed by eliminating and from the equation isAP EAMCET 2019 Easy
- Assuming \(|x|\) to be so small, that \(x^2\) and higher powers of \(x\) can be neglected, then \(\frac{\sqrt{1+x}+(1-x)^{3 / 2}}{(1+x)+\sqrt{1+x}}=\)AP EAMCET 2020 Medium
- Let \(f(x)=\cos (a x)+\sin (x)\) be periodic. Then \(a\) must beAP EAMCET 2020 Easy
- In \(\triangle A B C\), if \(A, B, C\) are in arithmetic progression then
\(\sqrt{\mathrm{a}^2-\mathrm{ac}+\mathrm{c}^2} \cdot \cos \left(\frac{\mathrm{~A}-\mathrm{C}}{2}\right)=\)AP EAMCET 2025 Medium - AP EAMCET 2018 Hard
- A straight line \(L\) with negative slope passes through the point \((1,1)\) and cuts the positive coordinate axes at the points \(A\) and \(B\). If \(O\) is the origin, then the minimum value of \(O A+O B\) as \(L\) varies, isAP EAMCET 2018 Easy
More PYQs from AP EAMCET
- \(\int \frac{1+x+\sqrt{x+x^2}}{\sqrt{x}+\sqrt{1+x}} d x\) is equal toAP EAMCET 2003 Medium
- If the average power per unit area delivered by an electromagnetic wave is , then the amplitude of the oscillating magnetic field in EM wave isAP EAMCET 2022 Medium
- The locus of mid-points of points of intersection of \(x \cos \theta+y \sin \theta=1\) with the coordinate axes isAP EAMCET 2022 Easy
- The number of three digit numbers in which 9 appears only in one place isAP EAMCET 2018 Easy
- If \(y=\operatorname{Tanh}^{-1} \sqrt{\frac{1-x}{1+x}}\), then \(\frac{d y}{d x}=\)AP EAMCET 2025 Medium
- In \(\triangle A B C\),
\((a-b)^2 \sin ^2\left(\frac{A+B}{2}\right)+(a+b)^2 \sin ^2\left(\frac{C}{2}\right)=\)AP EAMCET 2018 Medium