MHB Logarithm and harmonic numbers

[alyafey22]

I need to prove that

$$H_n = \ln n + \gamma + \epsilon_n $$

Using that

$$\lim_{n \to \infty} H_n - \ln n = \gamma $$

we conclude that

$$\forall \, \epsilon > 0 \,\,\,\, \exists k \,\,\,\, $$ such that $$\,\,\, \forall k \geq n \,\,\, $$ the following holds

$$|H_n - \ln n -\gamma | < \epsilon $$

$$H_n < \ln n +\gamma +\epsilon $$

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

 

[chisigma]

Re: logarithm and harmonic numbers

I need to prove that

$$H_n = \ln n + \gamma + \epsilon_n $$

Using that

$$\lim_{n \to \infty} H_n - \ln n = \gamma $$

we conclude that

$$\forall \, \epsilon > 0 \,\,\,\, \exists k \,\,\,\, $$ such that $$\,\,\, \forall k \geq n \,\,\, $$ the following holds

$$|H_n - \ln n -\gamma | < \epsilon $$

$$H_n < \ln n +\gamma +\epsilon $$

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

http://mathhelpboards.com/discrete-mathematics-set-theory-logic-15/difference-equation-tutorial-draft-part-i-426.html#post2494

Kind regards

$\chi$ $\sigma$

 

[alyafey22]

Re: logarithm and harmonic numbers

http://mathhelpboards.com/discrete-mathematics-set-theory-logic-15/difference-equation-tutorial-draft-part-i-426.html#post2494

Kind regards

$\chi$ $\sigma$

My friend this is amazing , I must have time to read that , keep it up .