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Infinite series with all negative terms

  1. Nov 14, 2015 #1

    I have been reviewing my textbook lately, and I came across a rather paradoxical statements. all of the convergence tests in my book state that the terms of the series has to be positive. However, when I solved this power series ∑(-1)n-1(xn/n), I found that it converges for -1<x≤1, but when I plugged -0.45 to test if the infinite series will converge, I got all the terms negative. So my question is can a series converge if all its terms are negative?
  2. jcsd
  3. Nov 14, 2015 #2


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    2017 Award

    Staff: Mentor

    Yes. E.g. ##-e##.
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