Aproximare parte fractionara
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Aproximare parte fractionara
Sa se arate ca \( \sum_{n\leq x}\left\{\frac{x}{n}\right\}=(1-\gamma)x+O(x^{1/2}) \), unde \( \{x\} \) reprezinta partea fractionara a numarului real \( x \), iar \( \gamma \) este constanta lui Euler.
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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Filip Chindea
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Vezi topicul de aici, si faceti observatia ca
\( \sum_{k=1}^n d(k) = \sum_{ab \le n} 1 = \sum_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \).
\( \sum_{k=1}^n d(k) = \sum_{ab \le n} 1 = \sum_{k=1}^n \left\lfloor \frac{n}{k} \right\rfloor \).
Life is complex: it has real and imaginary components.