Pentru orice \( k\geq 2 \) definim sirurile partiale armonice (sirurile k-armonice), \( H_{k}=\sum_{j=1}^{k}\frac{1}{j} \). Sa se calculeze
\( \sum_{k=2}^{\infty}\frac{(2k+1)H_{k}^{2}}{(k-1)k(k+1)(k+2)} \).
American Mathematical Monthly, 2007
Serie de calculat cu termeni ai sirului armonic
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Serie de calculat cu termeni ai sirului armonic
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.