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- 13:30, 8 January 2025 Andrei.Horvat talk contribs created page 14183 (Created page with "'''14183 (Gheorghe Szőllőssy)''' ''Să se calculeze suma <math>S = \displaystyle \sum_{k=0}^n \left(k+1\right)^2C_n^k</math>.'' '''Soluție''' Pentru orice număr natural <math>p</math> considerăm <math>S(p,n) = \displaystyle \sum_{k=0}^n k^pC_n^k</math>. Pentru orice număr natural <math>n</math> au loc egalitățile <math>S(0,n) = \displaystyle \sum_{k=0}^n C_n^k = 2^n</math> <math>S(1,n) = \displaystyle \sum_{k=0}^n kC_n^k = n2^{n-1}</math> <math>S(2,n) = \dis...")