Q. The value of $1 - \log 2 + \frac{\left( \log 2 \right)^{2}}{2!} - \frac{\left( \log 2 \right)^{3}}{3!} + \ldots$ is
A) $\log 3$
B) $\log 2$
C) $\frac{1}{2}$
D) None of these
Explanation
(c)
$\therefore 1 - \log{2 + \frac{\left( {\log 2}^{\ } \right)^{2}}{2!} - \frac{\left( \log 2 \right)^{3}}{3!} + \ldots = e^{- \log 2}\ }$
$= e^{\log 2^{- 1}} = \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.