Find the sum of [tex]\Sigma^{\infty}_{k=1}\frac{(-1)^{k+1}}{k}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

I know the series converges because the coefficients go monotonically to zero. However it's been a few years since I was taught how to sum these series, so I'm having trouble. I thought about telescoping, but no terms seem to cancel each other. I thought about maybe grouping terms together but I'm not sure how to proceed with that. I believe the sum should be ln(2), which implies those above methods aren't adequate. I was thinking maybe I need to compare the series with some other known series? A nudge in the right direction would be great, thanks.

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# Homework Help: Sum of alternating series

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