[tex]\displaystyle x+2x+...+100x=50500 \\ \\ x(1+2+...+100)=50500 \\ \\ x \cdot \frac{100(100+1)}{2} =50500 \\ \\ x \cdot \frac{100 \times 101}{2} =50500 \\ \\ x \cdot \frac{10100}{2} =50500 \\ \\ x \cdot 5050=50500 \\ \\ 5050x=50500 \\ \\ x= \frac{50500}{5050} \\ \\ x=10[/tex]
