Ah I fucked up, ignore what I asked. How do you solve part c? Thanks
Thanks a lot, I've never seen this used before
Postmax "You're Welcome"
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
Using the double angle formula seems more intuitive to me
Limit (1² + 2² + 3² + ... + n²)/n³
n---->infinity
n---->infinity
Guys what do you think of this guy's style?
1/6 because 1^2 + 2^2 + ... + n^2 = n(n+1)(2n+1)/6.
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
1/3, I think you forgot the 2n^2
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
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
Yeah I forgot the 2. Thanks for pointing it out.
@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.
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.
It's infinite series time baby
Does (-1) to the power of n, summation of all terms from 1 to infinity diverges or converges?
I haven't started yet, I'll answer this in a week or so.
not at all what I expected, but I'm all for it
It's the chapter after 'Parametric Equations and Polar Coordinates'.
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.
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.
yeah I doubt it really matters which book one uses
|r|=|-1|= 1>0
Therefore it is divergent.
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).
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.
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
Thanks
here's an actual proof. i guess i used some implicitly used some lemmas but i dont care
Thanks
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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Over for mathcels
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.
Which book if I may ask?
Since you're watching Michael Penn's videos now, I guess that means you matured mathematically. Congrats
Introduction to Real Analysis
Textbook by Robert G. Bartle
It was recommended to me by the Math Sorcerer, I still watch the Math Sorcerer though. I watch whoever helps me learn, but thanks for the compliment, I appreciate it.
@trying to ascend Turns out real analysis and calculus go hand in hand jfl
@Ahnfeltia His real analysis videos are great, it's helping me learn about proofs along with the "proofs" part of the book, love him.
Michael Penn you mean?
That guy
I've never watched his course videos, but the videos on his main channel are pretty OK. How do you like epsilon-delta arguments? Most students hate them.
Ah I see.
It was hard for me when I first read it. I stopped thinking about it for almost half a year, re-read the book and understood maybe 80% of it. Then I went to watch his videos to hear a verbal explanation of what's going on as well as to see how he constructs the proof.
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