Formula lui Gauss pentru sume de numere impare (suma incepe cu numarul 1) 1 + 3 + 5 + 7 + … + ( 2n – 1 ) = n x n 99 = 2n-1,  de unde 2n = 99 + 1=100 => n = 100 : 2 = 50 deci suma S = 50 x 50 = 2500

[latex]1+3+5+...+99 = sumlimits_{k=1}^{49}(2k+1) = sumlimits_{k=1}^{49}(2k) - sumlimits_{k=1}^{49}(1) = \ \ = 2cdot sumlimits_{k=1}^{49}(k)-(1+1+underset{ ext{de 49 ori}}{underbrace{...}}+1) = 2cdot (1+2+3+...+49)-49 = \ \ = 2cdot dfrac{49cdot (49+1)}{2}-49 = 49cdot (49+1)-49 = 49cdot 50-49 = \ \ = 49cdot (50-1) = 49cdot 49 = 49^2 = 2401[/latex]