Question

The sum of the series $S$ will be equal to

$\left(\frac{a-b}{a}\right)+\frac{1}{2}{\left(\frac{a-b}{a}\right)}^2+\frac{1}{3}{\left(\frac{a-b}{a}\right)}^3+...$

• A. ${\log }_{e}ab$
• B. ${\log }_e\frac{b}{a}$
• C. ${\log }_e\frac{a}{b}$
• D. ${\log }_e{a}^b$

Answer 1

Answer: (C)

${\log }_e\frac{a}{b}$

$(1-\frac{b}{a})+\frac{{(1-\frac{b}{a})}^2}{2}+\frac{{(1-\frac{b}{a})}^3}{3}+...\infty$
$=-\log (1-(1-\frac{b}{a}))$
$=-\log \left(\frac{b}{a}\right)$
$=\log \left(\frac{a}{b}\right)$