Hãy tìm x biết \(\begin{aligned} &x+(x+1)+(x+2)+(x+3)+\ldots+(x+2009)=2009.2010 \end{aligned}\)

Ta có:

\(\begin{aligned} &x+(x+1)+(x+2)+(x+3)+\ldots+(x+2009)=2009.2010 \\ &\Leftrightarrow 2010 x+(1+2+3+\ldots+2009)=2009.2010 \\ &\Leftrightarrow 2010 x+\frac{2009 .(2009+1)}{2}=2009.2010 \\ &\Leftrightarrow 2010 x=2009.2010-2009.2010: 2 \\ &\Leftrightarrow x=2009-2009: 2=1004,5 \end{aligned}\)