Hidden Roots Part 2

Calculus Level 5

F(x)=1x1+1x2+1x3++1x99+1x100\mathfrak{F}(x)=\dfrac{1}{x-1}+\dfrac{1}{x-2}+\dfrac{1}{x-3} + \ldots +\dfrac{1}{x-99}+\dfrac{1}{x-100}

Given the above function F(x)\mathfrak{F}(x) and

x1,x2,,xn\large x_{1},x_{2}, \ldots ,x_{n} are its roots in some order.

Find the maximum possible value of value
[x1][x2]+[x3][x4]+±[xn]n+1\large\dfrac{ [x_{1} ]-[ x_{2} ]+ [ x_{3} ]-[ x_{4} ]+ \ldots \pm[ x_{n} ]} {n+1}

Details and Assumptions

[m][m] represents greatest integer function of mm

Also try Hidden Roots
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