Absolute Convergence: Determining Convergence of (-1)^k*2^n/n^(n/2)

Thread starter kj13529
Start date Aug 5, 2007
Tags

Absolute

Aug 5, 2007

kj13529

I just want to verify my answers. I am asked to determine whether the sum converges absolutely, conditionally or diverges. ((-1)^k)*2^n)/n^(n/2). I got that it was conditionally convergent, is that correct?

Last edited: Aug 5, 2007

Physics news on Phys.org

Scientist returns to microbial roots and discovers potential quantum computing advancement
Physicists achieve record precision in measuring proton-to-electron mass ratio with H₂⁺
Quantum calculations provide a sharper image of subatomic stress

Aug 5, 2007

morphism

Science Advisor

Homework Helper

Why did you get that?

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

View full post »

Thread 'Solve this problem that involves induction'

Hello, This is the attachment, the steps to solution are pretty clear. I guess there is a mistake on the highlighted part that prompts this thread. Ought to be ##3^{n+1} (n+2)-6## and not ##3^n(n+2)-6##. Unless i missed something, on another note, i find the first method (induction) better than second one (method of differences).

View full post »