Here's a rly cool solution from stackexchange, which blows my average geometric solution out of the water
::: spoiler spoiler :::
I've shown that ln(n/n-1) is always larger than 1/n, so Σln(n/n-1) for all natural number n will be larger than the series 1+1/2+1/3+...
but I don't know how to make sure the sum of all ln(p/p-1) only when p is prime is larger than the provided series
the question is strongly suggesting its divergent, i just dont know how to show it
i pulled the image from a meme channel, so i dont know if its real or not, but at the same time, this below does look like a legit response
the background it likely ai generated anyways
(i took the meme off some discord channel, so i dont know how its made)
Hint: ::: spoiler spoiler It is not a telescoping series :::
Solution: ::: spoiler spoiler https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-18_not-a-telescoping-series.html :::
i got the answers, but i dont really know why
::: spoiler spoiler https://gmtex.siri.sh/fs/1/School/Extra/Maths/Challenges%20solutions/bound-f.html :::
Solution (starter question): ::: spoiler spoiler :::
Please refer to the main post, if you don't like looking at the image. https://gmtex.siri.sh/fs/1/School/Extra/Maths/Unsolved/1d-gravity.html
For the main question, you are encouraged to share your progress ::: spoiler spoiler
You might be able to solve this with differential equations, or by solving the iterative functions, I dont know :::
i added the solution to the post, i didnt see the multiplication before someone mentioned it, but yeah if we put it to the power of e it will telescope again, which is clearly the main character of this sub at this point (jk)
Solution:
::: spoiler spoiler https://gmtex.siri.sh/fs/1/School/Extra/Maths/Qotd%20solutions/2024-05-14_lnx-differential.html :::
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