Integral test and ratio test on haromonic series.

  • Thread starter avman
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  • #1
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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
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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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