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$\log_42-\log_82+\log_{16}2-\log_{32}2+...$
In the given solution, the answer is given as $1-\ln2$. How do I arrive at this solution? Thank you!

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Darshini Poola
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    "However, many sites claim that $1/2−1/3+1/4−1/5\ldots$ is an undefined value" -- Out of curiosity, could you please provide reference to at least one such site? – zipirovich Jan 31 '19 at 18:39

1 Answers1

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$\ln (1+x) = x - \frac{x^2}{2} + \frac{x^3}{3} - \dots \quad $, see series expansion

Put $x = 1 $ and you get the required form

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