S=sum of (-1)^n/n from 1 to infty
For why I named the post as so, here’s why
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ln(2) because the Taylor series for ln(1+x) evaluated at x=1 is exactly this series.
Good one. Thanks for posting!
yup thats the intended solution, im not really familiar with taylor series yet, but maybe for a person who knows taylor series would be able to see it right away
There closest I was able to do on the fly was to show that the ::: pairwise sum has an integral of -ln(2)/2 ::: but that was pretty hand wavy. I’ll have to check how it’s actually done.
Hint
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The solution I have in mind is related to the Taylor series
Hint 2
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It converges to -ln(2), but why
Solution:
![[2024/06/02] Horizontal asymptote of the other kind](https://lemmy.world/pictrs/image/257951ff-629c-44bc-ad36-af795ff303ad.png){kind=link}