Question

x+(x+1)+(x+2)+(x+3)+...(x+2003)=2004

Answer 1

<=> 2004x + (2003+1)x2003;2=2004

<=> 2004x = -2005002

<=> x= -1000,5

Answer 2

\(x+\left(x+1\right)+\left(x+2\right)+...+\left(x+2003\right)=2004\)

\(\Leftrightarrow x\times2003+\left(1+2+3+...+2003\right)=2004\)

\(\Leftrightarrow2003x+\frac{\left(1+2003\right)2003}{2}=2004\)

\(\Leftrightarrow2003\left(x+1002\right)=2004\)

\(x+1002=\frac{2004}{2003}\)

\(x=\frac{2004-2007006}{2003}=\frac{2005002}{2003}\)