log 2+215+13.53+15.55+……∞=

log 2+215+13 153+…… =log2+log1+151-15 =log2+log64 =log223=log3

log 2+215+13.53+15.55+……∞=

log 2+215+13 153+…… =log2+log1+151-15 =log2+log64 =log223=log3

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$\log 2 + 2 [\frac{1}{5} + \frac{1}{3 . 5^{3}} + \frac{1}{5 . 5^{5}} + \dots \dots \infty] =$

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$\log 2$

$\log 3$

$\log 5$

$\log 6$

answer is B.

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$\begin{array}{rcl} \log 2 + 2 [\frac{1}{5} + \frac{1}{3} {(\frac{1}{5})}^{3} + \dots \dots] \\ = & \log 2 + \log (\frac{1 + \frac{1}{5}}{1 - \frac{1}{5}}) \\ = & \log 2 + \log (\frac{6}{4}) \\ = & \log 2 (\frac{2}{3}) = \log 3 \end{array}$

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log 2+215+13.53+15.55+……∞=

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$\log 2 + 2 [\frac{1}{5} + \frac{1}{3 . 5^{3}} + \frac{1}{5 . 5^{5}} + \dots \dots \infty] =$