13-12.19+13.127-14.181……∞=

13-12132+13132..... =log 1+13=loge43

13-12.19+13.127-14.181……∞=

13-12132+13132..... =log 1+13=loge43

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$\frac{1}{3} - \frac{1}{2} . \frac{1}{9} + \frac{1}{3} . \frac{1}{27} - \frac{1}{4} . \frac{1}{81} \dots \dots \infty =$

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${loge}_{e} (2 / 3)$

$- {loge}_{e} (4 / 3)$

${loge}_{e} (4 / 3)$

$- {loge}_{e} (2 / 3)$

answer is C.

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Detailed Solution

$\begin{array}{rcl} \frac{1}{3} - \frac{1}{2} {(\frac{1}{3})}^{2} + \frac{1}{3} {(\frac{1}{3})}^{2} . . . . . \\ = & \log (1 + \frac{1}{3}) = \log_{e}^{(\frac{4}{3})} \end{array}$

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