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Series With Positive and Negative Terms

In this section we briefly state two results concerning series a n with terms a n that are not necessarily ≥ 0 . The first result has to do with absolute convergence and the second with alternating series.

  1. A series a n is said to converge absolutely if | a n| converges. It is a theorem that if any series converges absolutely, then it also converges.
  2. A series a n is said to be alternating if the a n alternate between being positive and negative. If a n is an alternating series such that | a n+1|≤| a n| for all n≥1 and a n = 0 , then a n converges. This is called the alternating series test.

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