teadawg1337

You have the answer? So this problem is taken from elsewhere? These are things that should be added to your question, especially the fact that you know the value of the series; answerers are here to help you, and saying that you know the answer without sharing it is antithetical to the collaborative nature of this site.

I haven't downvoted it personally, but it's likely because the question is very mathematically dense with no explanation between any of your steps. Also, saying that you "intuitively feel that [the series] is equal to zero" while also saying definitively at the end of your question that it is NOT zero with no further explanation is a bit odd. Your post will likely be received better with more explanation in key parts.

@BillDubuque The "in part or in whole" stipulation from the help page is what was mostly confusing me, but it makes sense to treat it the same as plagiarism in general. I thought it was much stricter, so I'll try to weigh if a post is transformative from now on before flagging.

It was my understanding from this very unambiguously-phrased help page that this shouldn't be allowed, but if my flag was declined then am I mistaken?

Hello, I'm a bit confused about the exact policy regarding LLM/genAI content after a flag I raised got declined regarding this answer here. They clearly state that they used Grok to make it, and they paraphrase in parts but in one part it contains a very egregious abuse of notation that suggests at least some of the content was taken directly from Grok.

I'll restate what I said before but later deleted: I'm uncertain if 2825 converges to a single digit because it's so much larger than 28. The convergence of 28 does not imply the convergence of 2825.

Working on a community wiki answer right now

It may be worth adding a community wiki answer that people can edit with contributions to whittle things down instead of clogging the comments. This will likely be merged to a chat room if it gets too cluttered.

$36$, $49$, $62$, $72$, $86$, $93$, $262$, and $729$ all converge to a sequence with $2825$ (see here and here), but that's as far as I'm able to go computationally. Most tools have an exponent limit of 64 bits.

An easier method would be to use $\sin{x}\cos{x}=1/2\, \sin(2x)$

Should I start a bounty on a question of mine that's been unanswered for the 17-ish days it's been up?

I suppose that gives me more time to work on mathematics :3

I'm super tired, I woke up early today

How are you all today?

Hello everyone o/

I'm aware of the joke, I just didn't realize it was a standalone statement at first

I thought it was in reference to the problem that was being worked on previously

@Ramanujan That's also not how you simplify fractions...

@Ramanujan Woah hold on, where are you getting 64/16?

Instead of using that identity, I believe it would be easier to observe the period of $\sin(\theta)$. The inclusion of $\pi$ in the problem isn't a coincidence

Oh dear, I just noticed that the textbook being used has the same notation issues

@DHMO The lack of parentheses in the original image

The notation is poor, but it's the same problem

Lol

Isn't sin(36) from a 3-4-5 triangle?

@SirCumference I'd need to reconsider my life decisions if I ever found myself being forced to calculate $\sin(39)$ by hand. In any practical setting, everyone would pick up a calculator for that. Why spend a good 30 seconds (at the very least) approximating it by hand if a calculator can give you the first 12 digits in less than a second?

Calculators are a replacement for performing needlessly tedious calculations. While I agree that using one to find out what 7*13 is (it's 91) would be ridiculous, it's also equally as ridiculous to expect people to be able to perform complex operations on the fly.

@TedShifrin I'll have to look into those sometime. I should probably get familiar with algebra first

@Ted I've started studying a bit of differential equations. Are there any other fields of mathematics that would somewhat suit the skill sets that I've developed with integrals?

It's an incredibly niche segment

Special functions

Well, not analysis

shrug

I'm pretty sure I've come to this realization several times already

@TedShifrin My progress in the field of analysis has pretty much reached an asymptote. I'm thinking it's time to branch out to other fields

Meh, it was worth a shot.

@Alessandro I'm not sure if this counts as a proof, but most large integers contain all digits from 0 to 9, so the number of terms excluded monotonically increases

Especially so now that it's starred

Hey there @Ted!

Multiplicative inverse

Exactly @Semiclassical

@s.harp I was joking as well

@s.harp I'd argue that the 1300's didn't have the same standards for mathematical rigor :P

@Mahmoud That's the harmonic series, which is proven to be divergent.

Yeah, it's bad

I think infinity can be defined as the lack of a definitive value

Is that a hint or the answer?

Are questions about integrals considered "out of style" nowadays?

Hello @Semiclassical

@DHMO No, that's the method I used