[tex]x+2x+3x+.....+100x=50500[/tex]
Dam factor comun pe x:
[tex]x*(1+2+3+...+100)=50500[/tex]
Calculam paranteza cu ajutorul sumei Gauss pentru numere consecutive:
[tex]x*(\frac{100*(100+1)}{2})=50500 \\ x*(\frac{100*101}{2})=50500 \\ x*(\frac{10100}{2})=50500 \\ x*5050=50500 \\ x=\frac{50500}{5050} \\ x=10[/tex]
