5

[2024/06/02] Horizontal asymptote of the other kind(lemmy.world)

posted
by
Avatar
siriusmart@lemmy.worldM
in
Avatar
dailymaths@lemmy.world
4 comments
hidereport

S=sum of (-1)^n/n from 1 to infty

For why I named the post as so, here’s why

spoiler

Sort:
HotTopControversialNewOld
Avatar
wisha@lemmy.ml
2 points
spoiler

ln(2) because the Taylor series for ln(1+x) evaluated at x=1 is exactly this series.

Good one. Thanks for posting!

permalink
report
reply
Avatar
siriusmart@lemmy.worldOPM
2 points

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

permalink
report
parent
reply
Avatar
quilan@lemmy.world
1 point
*

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.

permalink
report
reply
Avatar
siriusmart@lemmy.worldOPM
1 point
*

Hint

spoiler

The solution I have in mind is related to the Taylor series

Hint 2

spoiler

It converges to -ln(2), but why

Solution:

spoiler

https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd solutions/2024-06-02-alternating_harmonic.html

permalink
report
reply

Daily Maths Challenges

!dailymaths@lemmy.world

Create post

Share your cool maths problems.

Complete a challenge:

  • Post your solution in comments, if it is exactly the same as OP’s solution, let us know.
  • Have fun.

Post a challenge:

  • Doesn’t have to be original, as long as it is not a duplicate.
  • Challenges not riddles, if the post is longer than 3 paragraphs, reconsider yourself.
  • Optionally include solution in comments, let it be clear this is not a homework help forums.
  • Tag [unsolved] if you don’t have a solution yet.
  • Please include images, if your question includes complex symbols, attach a render of the maths.

Feel free to contribute to a series by DMing the OP, or start your own challenge series.

Community stats

  • 18

    Monthly active users

  • 34

    Posts

  • 35

    Comments

Community moderators