Recent content by TogoPogo

Thanks for your help. If I'm not mistaken, isn't ## \frac{1}{n^{\ln 2}} ## divergent? Or is there another series that I should be comparing to?

That's correct

Apologies, it should be as x approaches infinity... Thanks for the fix!

I am required to determine the convergence/divergence of the following series: $$ \sum_{n = 2}^{\infty} \frac{1}{(ln(n))^{ln(n)}}$$ Which test should I use? Wolfram Alpha says that the comparison test was used to determine that it was convergent, but I have no idea what series I should compare...

I got it! Thank you. I didn't know how to integrate secx but Wolfram helped out.

The problem states: "By using the substitution y=xu, show that the differential equation \frac{dy}{dx}=\frac{y+\sqrt{x^{2}+y^{2}}}{x}, x>0 can be reduced to the d.e. x\frac{du}{dx}=\sqrt{u^{2}+1}. Hence, show that if the curve passes through the point (1,0), the particular solution is given by...

Nevermind, it seems that the solution was online. Looks like factorization actually has something to do with the product of the line segments. http://www.cut-the-knot.org/arithmetic/algebra/ProductOfDiagonals.shtml#Solution However, I don't understand the part where it says "This is a...

Thanks, that made a lot of sense (surprisingly!). I'm going to go work on this for a while now and report back if I make some progress (unlikely lol) By the way, this is for a grade 11 IB math class. I think I'm overthinking the assignment a bit too much. I was thinking if I could just use...

Thanks! I guess the real problem that confuses me is how the factorization of z^n - 1 = 0 can be used to prove the theorem that the product of the distances is equal to n... EDIT: Is there any way to express the distance of, for example, |z0-z2| in terms of |z0-z1|? Or just expressing the...

There's a proof for de Moivre's on the Internet that shows you how raising cisx to the nth power is the same as cisnx

Homework Statement Hello, I am trying to simplify the inputted function here http://www.wolframalpha.com/input/?i=sqrt%282%29+sqrt%281-cos%28%282pi%28x-y%29%29%2Fn%29%29 which is \sqrt{2}\sqrt{1-cos[2\pi(x-y)/n]} to the form of 2sin[(x-y)\pi/n] Homework Equations Not sure The Attempt at a...

I don't quite understand the conjugate pair part. Could you give me an example for factoring z^{3}-1=0? I found the roots via de Moivre's to be 1, -\frac{1}{2}+\frac{\sqrt{3}}{2}i, and -\frac{1}{2}-\frac{\sqrt{3}}{2}i. Then would the factored form be...

Homework Statement Hey, I am attempting to fully factorize z^{n}-1=0 for all integers of n where n does not equal zero, and where z is a complex number in the form a+bi. The question asks to first factorize the equation when n=3,4,5. I know how to factorize when n=3 and 4, but I get stuck at...