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Unsolved Challenge Range of Root

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,802
Show that the equation $x(x+1)(x+2)\cdots(x+2020)-1=0$ has exactly one positive solution $x_0$ and prove that this solution $x_0$ satisfies $\dfrac{1}{2020!+10}<x_0<\dfrac{1}{2020!+6}$.