[tex]\displaystyle x+2x+3x+...+100x=10100 \\ \\ x(1+2+3+...+100)=10100 \\ \\ x \cdot \frac{100(100+1)}{2} =10100 \\ \\ x \cdot \frac{100 \cdot 101}{2} =10100 \\ \\ x \cdot 50 \cdot 101=10100 \\ \\ 5050x=10100 \\ \\ x= \frac{10100}{5050} \\ \\ x=2[/tex]
