\(1+5+9+...+x=501501\)
\(\Leftrightarrow\frac{\left(1+x\right).\left[\left(x-1\right)\div4+1\right]}{2}=501501\)
\(\Leftrightarrow\left(1+x\right).\left[\left(x-1\right)\div4+1\right]=501501.2\)
\(\Leftrightarrow\left(1+x\right).\left[\frac{x-1}{4}+1\right]=1003002\)
\(\Leftrightarrow\frac{x-1}{4}\left(1+x\right)+x+1=1003002\)
\(\Leftrightarrow\frac{x-1}{4}+\frac{x-1}{4}x+x=1003001\)
\(\Leftrightarrow\frac{x-1+x\left(x-1\right)+4x}{4}=1003001\)
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