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(L3 / synthesis.) Show that the sequence $$ u_n \ = \ \sum_{k=1}^n \frac{1}{k} - \ln n $$ converges. Its limit is denoted by \(\gamma\) and is called the Euler-Mascheroni constant. (Uses tools from the Comparison by equivalent and by \(O\) subsection and the Absolute convergence section ; appears here because of the structural sequence-series link.)
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