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- #1

- Jan 17, 2013

- 1,667

\(\displaystyle H_n = \ln n + \gamma + \epsilon_n \)

Using that

\(\displaystyle \lim_{n \to \infty} H_n - \ln n = \gamma \)

we conclude that

\(\displaystyle \forall \, \epsilon > 0 \,\,\,\, \exists k \,\,\,\, \) such that \(\displaystyle \,\,\, \forall k \geq n \,\,\, \) the following holds

\(\displaystyle |H_n - \ln n -\gamma | < \epsilon \)

\(\displaystyle H_n < \ln n +\gamma +\epsilon \)

I think I used the wrong approach , didn't I ?