Fie \( x_{n} = \{ {\sum_{k = 1}^{n}\frac {1}{\sqrt k} \} \). Aratati ca sirul \( (x_{n}) \) este dens in \( [0,1] \).
ONM, Lista scurta 2004, Daniel Petriceanu
Sir dens in [0,1]
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Bogdan Posa
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Sir dens in [0,1]
Last edited by Bogdan Posa on Wed Feb 20, 2008 11:05 pm, edited 1 time in total.
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Radu Titiu
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Vezi aici pe caz general http://www.mathlinks.ro/viewtopic.php?t=155843 la ultimul post al lui perfect_radio .
A mathematician is a machine for turning coffee into theorems.