Question

aflati-l pe X
2X+4X+6X+......2004X=1002x1003

Answer 1

2X(1+2+3+......+1002)=1002x1003
2Xx1002x1003:2=1002x1003
2Xx1005006:2=1005006
2Xx502503=1005006
2X=1005006:502503
X=502503:2
X=251251,5

Answer 2

$\displaystyle 2x+4x+6x+...+2004x=1002 \cdot 1003 \\ \\ 2x(1+2+3+...+1002)=1005006 \\ \\ 2x \cdot \frac{1002(1002+1)}{2} =1005006 \\ \\ 2x \cdot \frac{1002 \times 1003}{2} =1005006 \\ \\ 2x \cdot \frac{1005006}{2} =1005006 \\ \\ 2x \cdot 502503=1005006 \\ \\ 1005006x=1005006 \\ \\ x= \frac{1005006}{1005006} \\ \\ x=1$