let u_n = Σ_(k=1) ^n (1/k) −ln(n) 1) prove that (u_n )is convergent 2) let γ =lim_(n→+∞) u


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Question Number 41345 by maxmathsup by imad last updated on 05/Aug/18

$l e t u_{n} = \sum_{k = 1}^{n} \frac{1}{k} - l n (n)$ $1) p r o v e t h a t (u_{n}) i s c o n v e r g e n t$ $2) l e t γ = {l i m}_{n \to + \infty} u_{n} p r o v e t h a t 0 < γ < 1$
Commented byalex041103 last updated on 06/Aug/18

$I s i t \sum_{k = 1}^{n} (\frac{1}{k} - l n (n)) o r (\sum_{k = 1}^{n} \frac{1}{k}) - l n (n) ?$
Commented bymath khazana by abdo last updated on 07/Aug/18

$(\sum_{k = 1}^{n} \frac{1}{k}) - l n (n)$
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