Category:Alternating Series Test

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This category contains pages concerning Alternating Series Test:


Let $\sequence {a_n}_{N \mathop \ge 0}$ be a decreasing sequence of positive terms in $\R$ which converges with a limit of zero.

That is, let $\forall n \in \N: a_n \ge 0, a_{n + 1} \le a_n, a_n \to 0$ as $n \to \infty$


Then the series:

$\ds \sum_{n \mathop = 1}^\infty \paren {-1}^{n - 1} a_n = a_1 - a_2 + a_3 - a_4 + \dotsb$

converges.

Pages in category "Alternating Series Test"

The following 5 pages are in this category, out of 5 total.