\(1+2+3+4+...+x=8011\)
\(\Rightarrow\left(x+1\right)\left[\left(x-1\right):1+1\right]:2=8011\)
\(\Rightarrow\left(x+1\right)\left[\left(x-1\right)+1\right]:2=8011\)
\(\Rightarrow\left(x+1\right)\left(x-1+1\right)=8011\)
\(\Rightarrow\left(x+1\right)x=8011\cdot2\)
\(\Rightarrow\left(x+1\right)x=16022\)
\(\Rightarrow\text{ }x\approx126,1\)
Mà: \(x\in N\)
\(\Rightarrow\) không có x thỏa mãn
=>x(x+1)/2=8011
=>x^2+x=16022
=>x^2+x-16022=0
mà x nguyên
nên \(x\in\varnothing\)