Cum se face suma lui Gauss cu numere impare ? Explicati ,va rog, si dati un exemplu. Multumesc!

[tex]1+3+5+...+99 = \sum\limits_{k=1}^{50}(2k-1) = \sum\limits_{k=1}^{50}(2k) - \sum\limits_{k=1}^{50}(1) = \\ \\ = 2\cdot \sum\limits_{k=1}^{50}(k)-(1+1+\underset{\text{de 50 ori}}{\underbrace{...}}+1) = 2\cdot (1+2+3+...+50)-50 = \\ \\ = 2\cdot \dfrac{50\cdot (50+1)}{2}-50 = 50\cdot (50+1)-50 = 50\cdot 51-50 = \\ \\ = 50\cdot (51-1) = 50\cdot 50 = 50^2 = 2500[/tex]