Recent content by matt.qmar

Ah, Thanks for the heads up. I suppose I sort of took that for granted. Would http://en.wikipedia.org/wiki/Abel%27s_test#Abel.27s_test_in_complex_analysis works to show convergence for all z ≠ 1 on the boundary (in particular, at our point i ≠ 1), as the an's are monotonically decreasing? Some...

Ʃn=1∞ in/n = -log(1-i), woo hoo!

Ah! I see, and we have |i| = 1 but i ≠ 1 so there we go! Thanks a bunch. Factoring out the -1 seems to make it all go quite nicely.

Hey, I am trying to determine the convergence/divergence of Ʃn=1∞ in/n. I have tried all the tests I could think of (Comparison, Ratio, Root, nth term) and cannot determine it's convergence. If there was a formula, for say, the Mth partial sum SM then, if the limit as M → ∞ of SM...

Oh, right. Of course! We have a sigma algebra. Thanks again to clarifying exactly what conditions allow that the sigma algebra is generated by a set.

Thanks for the reply! So I can see how to get the open sets from unions and intersections of those sets (Part 1) But I'm not sure how to get all those sets from finitly many open sets (Part 2)... I can see how to grab the last two, but I'm not sure to form (a,b] and (-∞, b] from open sets...

Hi! We're given a set F, and F is the set of all finite unions of sets of the form (a,b], (-∞, b], (-∞,∞), and (a,∞), for real numbers a & b. I am trying to show that the sigma-algebra generated by F is actually the Borel algebra on the Reals. (recalling that the Borel algebra of the...