a-ba+12a-ba2+13a-ba3+……∞=

a-ba+12a-ba2+13a-ba3+……∞= =-log 1-aba =-log ba=log ab

a-ba+12a-ba2+13a-ba3+……∞=

a-ba+12a-ba2+13a-ba3+……∞= =-log 1-aba =-log ba=log ab

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$\frac{a - b}{a} + \frac{1}{2} {(\frac{a - b}{a})}^{2} + \frac{1}{3} {(\frac{a - b}{a})}^{3} + \dots \dots \infty =$

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$\log_{e} (ab)$

$\log_{e} a . \log_{e} b$

$\log_{e} (a / b)$

answer is C.

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Detailed Solution

$\frac{a - b}{a} + \frac{1}{2} {(\frac{a - b}{a})}^{2} + \frac{1}{3} {(\frac{a - b}{a})}^{3} + \dots \dots \infty = = - \log (1 - \frac{ab}{a}) = - \log (\frac{b}{a}) = \log (\frac{a}{b})$

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