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Integral test and ratio test on haromonic series.

  1. Aug 9, 2012 #1
    So harmonic series diverges because of the integral test but if I try it on ratio test

    = (1 / ( x+1 )) / (1 / x)
    = x / (x + 1) and this is less than 1 so shouldn't it converge?
     
  2. jcsd
  3. Aug 9, 2012 #2
    The limit as x goes to infinity is 1, so the ratio test is inconclusive. It does not tell us whether the harmonic series converges or diverges.
     
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