Integral test and ratio test on haromonic series.

avman

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?

Millennial

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.