[2024/06/02] Horizontal asymptote of the other kind
S=sum of (-1)^n/n from 1 to infty
For why I named the post as so, here's why ::: spoiler spoiler :::
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S=sum of (-1)^n/n from 1 to infty
For why I named the post as so, here's why ::: spoiler spoiler :::
::: spoiler spoiler 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
Hint ::: spoiler spoiler The solution I have in mind is related to the Taylor series :::
Hint 2 ::: spoiler spoiler It converges to -ln(2), but why :::
Solution: ::: spoiler spoiler https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-06-02-alternating_harmonic.html :::
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.