Serie de calculat cu termeni ai sirului armonic
Posted: Wed Jan 09, 2008 3:57 am
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
\( \sum_{k=2}^{\infty}\frac{(2k+1)H_{k}^{2}}{(k-1)k(k+1)(k+2)} \).
American Mathematical Monthly, 2007