Question

x+2x+3x+.......+100x=5050

Answer 1

x+2x+3x+.......+100x=5050
x(1+2+3+.......+100)=5050
x*100(100+1)/2=5050
x*50*101=5050
5050x=5050
x=5050/5050
x=1

Answer 2

$\displaystyle x+2x+3x+...+100x=5050 \\ \\ x(1+2+3+...+100)=5050 \\ \\ x \cdot \frac{100(100+1)}{2} =5050 \\ \\ x \cdot \frac{100 \cdot 101}{2} =5050 \\ \\ x \cdot \frac{10100}{2} =5050 \\ \\ x \cdot 5050=5050 \\ \\ x=5050:5050 \\ \\ x=1$