Recent content by two lock

I'm not sure why that wouldn't converge at z=1. As k increases infinitely, shouldn't 1/k become infinitely small? Isn't saying that like saying that the sequence: (\frac{1}{n})^{∞}_{n=1} doesn't converge? Or does it actually not?

Well when z=-2, we get: ∞ \sum1k2=1+1+...+1=∞ as k→∞ k=0 So ak does not tend toward zero. Then at z=-3+i: ∞ \sumik2 k=0 So again, ak does not tend toward zero. In general, we can see that for any z such that z+3≥1, ak will not approach 0 as k increases towards infinity. That's a huge help...

Well that's partially why I used this example. I'm not sure how to handle when the exponent on the complex number is not just k. I realize now I made a mistake in the original post (I didn't make it on my problem set). If I'm right and the radius is 1, then what I meant to write was that z=-2...

Homework Statement I have a problem set that asks me to determine, first, the radius of convergence of a complex series (using the limit of the coefficients), and second, whether or not the series converges anywhere on the radius of convergence. Homework Equations As an example: Σ(z+3)k2 with...