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SuicideFuel Math thread problem (official)

trying to ascend

trying to ascend

Oldcel KHHV
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r = 3/4R.

P = weight of each sphere.

Find the value of the weight of the cylinder, such that the system is at rest
 
Fallenleaves

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a) it actually converges to 0.
b) it actually converges to 1/4
c) it converges to pi/4. not -1/3.
Why can't we approximate the integral of part c to be 1/x^4
 
CountBleck

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It's quite long, you'd still have to integrate cosine squared x
it would be a pain to overleaf anymore, but it's a simple method. you could either use IBP or just use the double angle formula
 
Fallenleaves

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it would be a pain to overleaf anymore, but it's a simple method. you could either use IBP or just use the double angle formula
Using the double angle formula seems more intuitive to me
 
trying to ascend

trying to ascend

Oldcel KHHV
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Limit (1² + 2² + 3² + ... + n²)/n³
n---->infinity
 
Fallenleaves

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Guys what do you think of this guy's style?
 
Fallenleaves

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I only watched the first few minutes. Not my cup of tea. Too whimsical for my liking.
I like his style a lot, what are the types of teaching styles that you like
 
trying to ascend

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You mean 2n^3. Because its the cubic term that gives 2.
2n² or 2n³, the result is the same, I just said 2n² because you can simplify it (n(n + 1)(2n + 1))/6n³
 
Caesercel

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2n² or 2n³, the result is the same, I just said 2n² because you can simplify it (n(n + 1)(2n + 1))/6n³
If you simplify, all the other powers of n will disappear after the limit. Only 2 remains because its the coefficient of cubic term (2n^3). Because it'll cancel out with the n^3 at bottom leaving a 2
 
Fallenleaves

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@Ahnfeltia Is it normal to continue to partial differentiation after learning first order ODE's?

The DE YouTube Playlist continues to partial differentiation after teaching ODE's but the book continues to parametric functions and so on before reaching the chapter about partial differentiation.
 
Ahnfeltia

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@Ahnfeltia Is it normal to continue to partial differentiation after learning first order ODE's?

The DE YouTube Playlist continues to partial differentiation after teaching ODE's but the book continues to parametric functions and so on before reaching the chapter about partial differentiation.
While I don't think it much matters, PDEs (partial differential equations) are usually considered a more advanced topic than parametric functions in my experience. The beauty is self-study, however, is that you get to study what you want in whatever order you want. I don't think you really need one to study the other, so just go with whatever order floats your boat I would say.
 
Fallenleaves

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While I don't think it much matters, PDEs (partial differential equations) are usually considered a more advanced topic than parametric functions in my experience. The beauty is self-study, however, is that you get to study what you want in whatever order you want. I don't think you really need one to study the other, so just go with whatever order floats your boat I would say.
It's infinite series time baby
 
Fallenleaves

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You got one of them big calculus books then?
It's the one by Stewart, it's an ebook. I've also downloaded another Calculus book but it's by Larson.
 
Ahnfeltia

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It's the one by Stewart, it's an ebook. I've also downloaded another Calculus book but it's by Larson.
my calculus book in uni was the one by Adam & Essex
 
Fallenleaves

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my calculus book in uni was the one by Adam & Essex
I see, I wonder what differences there could be between commonly used Calculus books in universities, they must be minimal I suppose.
 
Ahnfeltia

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I see, I wonder what differences there could be between commonly used Calculus books in universities, they must be minimal I suppose.
yeah I doubt it really matters which book one uses
 
Fallenleaves

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It diverges, but I didn't understand your reasoning
I'm treating this as a geometric series, where r = -1 is the common ratio. Take the absolute value of r and It's larger than or equal to one (I made a mistake by writing larger than 0 in the previous post).
 
Fallenleaves

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It diverges, but I didn't understand your reasoning
Is there a better way to prove? How's this: We take the limit of (-1) to the power n as n tends to infinity which diverges (the value of the limit oscillates between 1 and -1). As the value of the limit taken is not 0, by contradiction, the series is not convergent (divergent).

It isn't formal but yeah it's honest work.
 
trying to ascend

trying to ascend

Oldcel KHHV
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Is there a better way to prove? How's this: We take the limit of (-1) to the power n as n tends to infinity which diverges. As the value of the limit taken is not 0, by contradiction, the series is not convergent (divergent).

It isn't formal but yeah it's honest work.
This doesn't work, harmonic series approaches zero and it's divergent.

If it's convergent, it approaches zero, but the other way around isn't true.

The better would say that it's infinite and we can't know what value it will aproach, therefore it diverges
 
Fallenleaves

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This doesn't work, harmonic series approaches zero and it's divergent.

If it's convergent, it approaches zero, but the other way around isn't true.

The better would say that it's infinite and we can't know what value it will aproach, there it diverges
Thanks
 
Ahnfeltia

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here's an actual proof. i guess i used some implicitly used some lemmas but i dont care
View attachment 692105
the easier way to see it is to look at the sequence of partial sums, which goes -1, 0, -1, 0, -1, 0, ..., which is clearly not convergent as it's alternating
@Fallenleaves
 
Fallenleaves

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the easier way to see it is to look at the sequence of partial sums, which goes -1, 0, -1, 0, -1, 0, ..., which is clearly not convergent as it's alternating
@Fallenleaves
Is it possible for me to go into real analysis fully considering that I've barely learnt the content of infinite series and sequences in the calculus book?

I'm not interested in reading through all the convergent/divergent tests, I want to learn/read proofs in real analysis.

Scrap this question, I'll learn both at the same time.
 
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Fibroga

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Over for mathcels
 
Ahnfeltia

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Scrap this question, I'll learn both at the same time.
As far as I can tell, real analysis is very different from all the other math you're used to, so be prepared for that I guess. Good luck
 
Fallenleaves

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As far as I can tell, real analysis is very different from all the other math you're used to, so be prepared for that I guess. Good luck
Thanks.

I've read some parts of the book with the aid of Michael Penn's videos, funny twist of fate huh, I unsubscribed and now I'm watching his real analysis videos for help.
 

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