Part 6

Number Theory Level pending

Calculate: \[\left \lfloor \frac{1^2 + 1 + 1 }{1\times 2}+\frac{2^2 + 2 + 1}{2\times 3} + \ldots \frac{ n^2 + n + 1 } { n \times (n+1)} + \ldots +\frac{4066273}{4066272} \right \rfloor.\]

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