Question

$0.5 - \frac{(0.5)^{2}}{2} + \frac{(0.5)^{3}}{3} - \frac{(0.5)^{4}}{4} + ........$

• A. $\log_{e}\left( \frac{3}{2} \right)$
• B. $\log_{10}\left( \frac{1}{2} \right)$
• C. $\log_{e}(n!)$
• D. $\log_{e}\left( \frac{1}{2} \right)$

Answer 1

Answer: (A)

$\log_{e}\left( \frac{3}{2} \right)$

Answer 2

We know that, $x - \frac{x^{2}}{2} + \frac{x^{3}}{3} - \frac{x^{4}}{4}........\infty = \log_{e}(1 + x)$

Putting x = 0.5, we get,

$0.5 - \frac{(0.5)^{2}}{2} + \frac{(0.5)^{3}}{3} - \frac{(0.5)^{4}}{4} + ........\infty = \log_{e}(1 + 0.5) = \log_{e}\left( \frac{3}{2} \right)$