this post was submitted on 26 Mar 2024
118 points (87.8% liked)
Asklemmy
43908 readers
1339 users here now
A loosely moderated place to ask open-ended questions
Search asklemmy ๐
If your post meets the following criteria, it's welcome here!
- Open-ended question
- Not offensive: at this point, we do not have the bandwidth to moderate overtly political discussions. Assume best intent and be excellent to each other.
- Not regarding using or support for Lemmy: context, see the list of support communities and tools for finding communities below
- Not ad nauseam inducing: please make sure it is a question that would be new to most members
- An actual topic of discussion
Looking for support?
Looking for a community?
- Lemmyverse: community search
- sub.rehab: maps old subreddits to fediverse options, marks official as such
- !lemmy411@lemmy.ca: a community for finding communities
~Icon~ ~by~ ~@Double_A@discuss.tchncs.de~
founded 5 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
Great. Can you give me example of decreasing trend slower than that function curve?, where summation doesn't give finite value? A simple example please, I am not math scholar.
So, for starters, any exponentiation "greater than 1" is a valid candidate, in the sense that 1/(n^2), 1/(n^3), etc will all give a finite sum over infinite values of n.
From that, inverting the exponentiation "rule" gives us the "simple" examples you are looking for: 1/โn, 1/โ(โn), etc.
Knowing that
โn = n^(1/2), and so that 1/โn can be written as 1/(n^(1/2)), might help make these examples more obvious.Hang on, that's not a decreasing trend. 1/โ4 is not smaller, but larger than 1/4...?
From 1/โ3 to 1/โ4 is less of a decrease than from 1/3 to 1/4, just as from 1/3 to 1/4 is less of a decrease than from 1/(3ยฒ) to 1/(4ยฒ).
The curve here is not mapping 1/4 -> 1/โ4, but rather 4 -> 1/โ4 (and 3 -> 1/โ3, and so on).