Recent content by Chipz

Thank you for your help. After I realized that it was the negative of the Harmonic series, I realized I could use the same form of adding values consecutively to be a negative with an even denominator. So that I could simply divide by 2 to get the original sequence rendering (...permuted...

So since... 1+\frac{-1}{3} + \frac{-1}{2} + \frac{-1}{5} + \frac{1}{4} is not equal to the original series it's not absolutely convergent. That makes sense. I am familiar with Is there an appropriate nomenclature for describing this? Could you point me to a more formalized proof...

Homework Statement Show that the series \displaystyle\Sigma_{n=1}^{\infty} \frac{(-1)^n}{n} is not absolutely convergent. Do so by permuting the terms of the series one can obtain different limits. Homework Equations The Attempt at a Solution I don't have a total solution...

That's essentially the proof I gave. Although I've revised it a little to be more true for subsequences rather than partial sums. Let (n_1>n_2>n_3...) \in \mathbb{N} Suppose lim x_n = x given any \epsilon > 0 we must find an N s.t. j \ge N then |x_n_j - x| < \epsilon \forall n \ge N...

When does a position function hit the z axis? When the y and x-axis are 0.

Homework Statement Suppose that (x_n) is a sequence in a compact metric space with the property that every convergent subsequence has the same limit x. Prove that x_n \to x as n\to \infty Homework Equations Not sure, most of the relevant issues pertain to the definitions of the space...