3-1+123-12+133-13+……∞

3-1+123-12+133-13+…… =-log1-3-1 =log2-3-1=log12-3 =log2+3

3-1+123-12+133-13+……∞

3-1+123-12+133-13+…… =-log1-3-1 =log2-3-1=log12-3 =log2+3

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$(\sqrt{3} - 1) + \frac{1}{2} {(\sqrt{3} - 1)}^{2} + \frac{1}{3} {(\sqrt{3} - 1)}^{3} + \dots \dots \infty$

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$\log 2$

$\log (3 + \sqrt{2})$

$\log (2 + \sqrt{3})$

answer is D.

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Detailed Solution

$\begin{array}{rcl} (\sqrt{3} - 1) + \frac{1}{2} {(\sqrt{3} - 1)}^{2} + \frac{1}{3} {(\sqrt{3} - 1)}^{3} + \dots \dots \\ = & - \log (1 - (\sqrt{3} - 1)) \\ = & \log {(2 - \sqrt{3})}^{- 1} = \log (\frac{1}{2 - \sqrt{3}}) \\ = & \log (2 + \sqrt{3}) \end{array}$