Evaluate the sum of the series: $\log_e \frac{4}{5} + \frac{1}{4} - \frac{1}{2} \left( \frac{1}{4} \right)^2 + \frac{1}{3} \left( \frac{1}{4} \right)^3 - \dots$
- A$2 \log_e \frac{4}{5}$
- B$\log_e \frac{5}{4}$
- C$1$
- D$0$
Explore More
Similar Questions
$\cosh^{-1} 2 = $
$1+\frac{1}{3 \cdot 2^2}+\frac{1}{5 \cdot 2^4}+\frac{1}{7 \cdot 2^6}+\ldots$ is equal to
If $|a| < 1$ and $b = \sum_{k=1}^{\infty} \frac{a^k}{k}$,then $a$ is equal to
DifficultAP EAMCET 2005
View SolutionIf $\alpha, \beta$ are the roots of the equation $x^2 - px + q = 0$,then $\log_e(1 + px + qx^2) = $
Medium
View SolutionIf $0 < x < 1$ and $y = \frac{1}{2} x^{2} + \frac{2}{3} x^{3} + \frac{3}{4} x^{4} + \dots$,then the value of $e^{1+y}$ at $x = \frac{1}{2}$ is:
DifficultJEE MAIN 2021
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo