Question

1+10+100+...+100 de termeni -suma lui Gaus

Answer 1

 

Aceasta suma nu se calculeaza cu formula lui Gauss pentru ca nu este o progresie aritmetica.

[tex]\displaystyle\\ \underbrace{1+10+100+........}_{\text{100 de termeni}} =\\\\ =10^0+10^1+10^2+\cdots +10^{99}=\frac{10^{99+1}-1}{10-1}=\boxed{\frac{10^{100}-1}{9}}=\\\\ =\frac{1\!\overbrace{000.......000}^{\text{100 de zerouri}}-1}{9}= \frac{\overbrace{999.....999}^{\text{100 de nouri}}}{9}= {\underbrace{111......111}_{\text{100 de unuri}}[/tex]