# Hidden Roots Part 2

Calculus Level 5

$$\mathfrak{F}(x)=\dfrac{1}{x-1}+\dfrac{1}{x-2}+\dfrac{1}{x-3} + \ldots +\dfrac{1}{x-99}+\dfrac{1}{x-100}$$

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

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

Find the maximum possible value of value
$\large\dfrac{ [x_{1} ]-[ x_{2} ]+ [ x_{3} ]-[ x_{4} ]+ \ldots \pm[ x_{n} ]} {n+1}$

Details and Assumptions

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

×