Talk:Alternating series

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Mathematics rating:	Start Class	Low Priority	Field: Analysis
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. this article has a lot of room for improvement, take a look at any elementary calculus text.--Cronholm144 04:05, 14 May 2007 (UTC)

[edit] Wrong statement

The sequence of positive a_n's must be monotone decreasing after a certain point in order for the series to converge. Even then, the Liebniz's test is not an if and only if. For the first case, notice that a_n = 1/n if n is odd and a_n = 1/2^n if n is odd can be made to a divergent alternating series even though the limit as n tends to infinity of a_n is 0.

[edit] proof of Leibniz test

Anyone care to add a short proof of the Leibniz Test? I think it would add a lot to the page. Lavaka 05:45, 21 September 2006 (UTC)

I added a proof the way it came to my mind. In some texts it is a little more convoluted, although I think in the form stated here it is easy to see the idea of what's going on. Tinchote 5:17, 30 August 2007 (UTC)