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Question: The value of \(1 - \log 2 + \frac{(\log 2)^{2}}{2!} - \frac{(\log 2)^{3}}{3!} + ....\) is....

The value of 1−log⁡2+(log⁡2)22!−(log⁡2)33!+....1 - \log 2 + \frac{(\log 2)^{2}}{2!} - \frac{(\log 2)^{3}}{3!} + .... is.

A

2

B

12\frac{1}{2}

C

log⁡3\log 3

D

None of these

Answer

12\frac{1}{2}

Explanation

Solution

Given series

=log⁡e4\log_{e}4

=e−log⁡2=elog⁡(12)= e ^ { - \log 2 } = e ^ { \log \left( \frac { 1 } { 2 } \right) } log⁡e12\log_{e}\frac{1}{2}.