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Ratio Test

  • Definition: Given a series sum(a_n) of nonzero complex number terms,let r= lim inf |a_(n+1)/a_n|, R= lim sup |a_(n+1)/a_n|. a) The series sum(a_n) converges absolutely if R < 1. b) The series sum(a_n) diverges if r > 1. c) The test is inconclusive if r<= 1 <= R.

    Source: Mathematical Analysis, second edition by Tom M. Apostol

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