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Series With Positive and Negative Terms

Series With Positive and Negative Terms

Series With Positive and Negative Terms

Series With Positive and Negative Terms

Series With Positive and Negative Terms

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.