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Evaluate $\sum_{n=1}^{\infty }\ln \left (\frac{7^n+1}{7^n} \right )$ .

Found this question on Art of Problem Solving. It was stuck in the "solved" section, but I couldn't find a solution, and I myself am stumped.

Apparently it could also be simplified to $\sum_{k=0}^{\infty }\frac{\left ( -1 \right )^{k+1}}{k\left ( 7^{k}-1 \right )}$ , but I don't follow this either.

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    AOPS say $$\sum_{n=1}^{\infty} \ln \left( \frac{7^n+1}{7^n} \right)$$2012-03-06
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    @SivaramAmbikasaran: I see. Very strange of OP to miss that!2012-03-06
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    You'll want $k$ to go from $1$ to $\infty$, not from $0$.2012-03-06
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    @SivaramAmbikasaran I'm new to LaTeX. Give me a bit of leniency. :P2012-03-06

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