[tex]\displaystyle x+2x+3x+...+100x=5050 \\ \\ x(1+2+3+...+100)=5050 \\ \\ x \cdot \frac{100(100+1)}{2} =5050 \\ \\ x \cdot \frac{100 \cdot 101}{2} =5050 \\ \\ x \cdot \frac{10100}{2} =5050 \\ \\ x \cdot 5050=5050 \\ \\ x=5050:5050 \\ \\ x=1 \\ Am~aplicat~suma~lui~Gauss: \frac{n(n+1)}{2} [/tex]
