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(B) We have $\log_e x - \log_e (x - 1) = \log_e \left( \frac{x}{x - 1} \right)$.This can be written as $\log_e \left( \frac{1}{1 - \frac{1}{x}} \right

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$\frac{1}{x} + \frac{1}{2x^2} + \frac{1}{3x^3} + \dots \infty $

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(B) We have $\log_e x - \log_e (x - 1) = \log_e \left( \frac{x}{x - 1} \right)$.This can be written as $\log_e \left( \frac{1}{1 - \frac{1}{x}} \right) = -\log_e \left( 1 - \frac{1}{x} \right)$.Using the logarithmic expansion series $-\log_e (1 - y) = y + \frac{y^2}{2} + \frac{y^3}{3} + \dots$ where $y = \frac{1}{x}$,we get:$-\log_e \left( 1 - \frac{1}{x} \right) = \frac{1}{x} + \frac{1}{2x^2} + \frac{1}{3x^3} + \dots \infty$.

$\log_e x - \log_e (x - 1) = $

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