integral test, root test, alternating series test were the most difficult part for me in Calculus II. Professor didn't bother explaining these test drawing on the board. After watching this, I now have much clear and better understanding.
The proofs are fairly easy once you sit down and properly read them through. Even if you don't follow the proofs, it's easy to apply these tests without actually knowing what they mean. It's literally just a checklist for convergence/divergence.
lol, wish this was up when I was in Calculus I ! XD Oh well, still need the refresher anyways. ;) Understanding it, and not forgetting it is always important.
1/x does not pass the integral test. The integral of this function also diverges, since the integral is ln(x) + C, instead of being a power function of x. This leads to the paradox of Gabriel's Horn, where a body of revolution from y=1/x from x=1 to infinity defines the shape of a horn with a finite volume, and an infinite surface area.
Why the divergent harmonic series cannot proof Zeno Paradox of movement? Why is proved with the series of 1/2^n and not with that of 1/n if both sequences tends to 0 ? Ok series 1/2^n is convergent and our harmonic divergent, but if Zeno asked for 1/2, 1/3 ,1/4, 1/5 ,...,1/n to the destination, this divergent is one case Against the other convergent used to proof of movement. Is not a "math cheat" choose one sequence convenient to the proof without explain why others are not valid AGAINST that choosen? If the answer is only :"divergent is infinite sum" this gives reason to Zeno, as he have one valid infinite sum against that convergent proof. Who wins? I think have math answer to this, but post my initial fair though. PS: i see in the convergent as in each step summing 1/2^n to the acquired also remains 1/2^n to destination, as in the harmonic summing 1/n to the acquired remains (1-1/n) to destination.
integral test, root test, alternating series test were the most difficult part for me in Calculus II. Professor didn't bother explaining these test drawing on the board. After watching this, I now have much clear and better understanding.
The proofs are fairly easy once you sit down and properly read them through. Even if you don't follow the proofs, it's easy to apply these tests without actually knowing what they mean. It's literally just a checklist for convergence/divergence.
Thank you for your time and your excellent way to teach👍🏻
thank you very much from my heart
i learned much and my skills doubled from your tutorial
Thank you sir for your dedication! 🙏
Teacher: -you have 24h to prepare for this topic.
Me watching Dave: nah 10m is plenty of time for learning this.
P.S. Another awesome video.
brilliant. as usual.
Thanks for all your work. You're a Jedi sir
Your explanation is really helpful
Thank sir for this explanation.......
Nice explanation!
lol, wish this was up when I was in Calculus I ! XD Oh well, still need the refresher anyways. ;) Understanding it, and not forgetting it is always important.
Thank you for the awesome explanation, professor!!
Please come teach at my university...they make these things seem so abstract while they are in fact very intuitive
You're amazing!!
he knows a lot about all kinds of stuff
Epic Win Uncle Dave
He's my Papa
Awesome
Check at video time around 3 Minute. Limit is 2, infinity not 1 , infinity. Please correct it.
Sir,as u showed that 1/(x^2) is covergent then even 1/x should also be convergent but it is diverging. Sir please tell how❓
check out my tutorial on improper integrals and it will make more sense!
1/x does not pass the integral test. The integral of this function also diverges, since the integral is ln(x) + C, instead of being a power function of x. This leads to the paradox of Gabriel's Horn, where a body of revolution from y=1/x from x=1 to infinity defines the shape of a horn with a finite volume, and an infinite surface area.
thank you calc jesus
IIT
Why adding 1 to the integral?
The series is 1 + 1/4 + 1/8 + ...
Why the divergent harmonic series cannot proof Zeno Paradox of movement? Why is proved with the series of 1/2^n and not with that of 1/n if both sequences tends to 0 ? Ok series 1/2^n is convergent and our harmonic divergent, but if Zeno asked for 1/2, 1/3 ,1/4, 1/5 ,...,1/n to the destination, this divergent is one case Against the other convergent used to proof of movement. Is not a "math cheat" choose one sequence convenient to the proof without explain why others are not valid AGAINST that choosen? If the answer is only :"divergent is infinite sum" this gives reason to Zeno, as he have one valid infinite sum against that convergent proof. Who wins? I think have math answer to this, but post my initial fair though. PS: i see in the convergent as in each step summing 1/2^n to the acquired also remains 1/2^n to destination, as in the harmonic summing 1/n to the acquired remains (1-1/n) to destination.
find the Summation of 1/√n 😐
It's divergent 🙃
I'm so so so stupide to understand this .. juste i can't get it .
Yes i know I'm suck on maths , very suck
:/